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of Filters for the Navier-Stokes Equation", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-070159561", id = "record", doi = "10.48550/arXiv.1110.2527" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20170612-123329512, title = "Convergence Analysis of the Ensemble Kalman Filter for Inverse Problems: the Noisy Case", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-123329512", id = "record" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161221-112013537, title = "Analysis of the ensemble Kalman filter for inverse problems", journal = "SIAM Journal on Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161221-112013537", id = "record", issn = "0036-1429", doi = "10.1137/16M105959X", volume = "55" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161221-105527857, title = "Quasi-Monte Carlo and Multilevel Monte Carlo Methods for Computing Posterior Expectations in Elliptic Inverse Problems", journal = "SIAM/ASA Journal on Uncertainty Quantification", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161221-105527857", id = "record", issn = "2166-2525", doi = "10.1137/16M1061692", volume = "5" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161220-181119556, title = "Geometric MCMC for Infinite-Dimensional Inverse Problems", journal = "Journal of Computational Physics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161220-181119556", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2016.12.041", volume = "335" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161221-112623998, title = "Derivation and analysis of simplified filters", journal = "Communications in Mathematical Sciences", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161221-112623998", id = "record", issn = "1539-6746", doi = "10.4310/CMS.2017.v15.n2.a6", volume = "15" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161221-113147238, title = "Filter Based Methods For Statistical Linear Inverse Problems", journal = "Communications in Mathematical Sciences", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161221-113147238", id = "record", issn = "1539-6746", doi = "10.4310/CMS.2017.v15.n7.a4", volume = "15" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20161111-104641272, title = "Handbook of Uncertainty Quantification", chapter = "The Bayesian Approach to Inverse Problems", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161111-104641272", id = "record", isbn = "978-3-319-12384-4", doi = "10.1007/978-3-319-12385-1\_7" } @other{https://resolver.caltech.edu/CaltechAUTHORS:20161220-182307792, title = "Gaussian approximations for transition paths in molecular dynamics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161220-182307792", id = "record", doi = "10.48550/arXiv.1604.06594" } @book{https://resolver.caltech.edu/CaltechAUTHORS:20161110-160355297, title = "Matrix Analysis and Algorithms", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161110-160355297", id = "record" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170113-072909521, title = "The Bayesian formulation of EIT: Analysis and algorithms", journal = "Inverse Problems and Imaging", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170113-072909521", id = "record", issn = "1930-8345", doi = "10.3934/ipi.2016030", volume = "10" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-142444027, title = "MAP estimators for piecewise continuous inversion", journal = "Inverse Problems", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-142444027", id = "record", issn = "0266-5611", doi = "10.1088/0266-5611/32/10/105003", volume = "32" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160715-152128338, title = "Filter accuracy for the Lorenz 96 model: fixed versus adaptive observation operators", journal = "Physica D: Nonlinear Phenomena", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160715-152128338", id = "record", issn = "0167-2789", doi = "10.1016/j.physd.2015.12.008", volume = "325" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161111-103206810, title = "Mathematics, Statistics and Data Science", journal = "EMS Newsletter", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161111-103206810", id = "record", issn = "1027-488X", volume = "100" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160715-161420502, title = "A Function Space HMC Algorithm With Second Order Langevin Diffusion Limit", journal = "Bernoulli", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160715-161420502", id = "record", issn = "1350-7265", doi = "10.3150/14-BEJ621", volume = "22" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161221-114630868, title = "A Bayesian Level Set Method for Geometric Inverse Problems", journal = "Interfaces and Free Boundaries", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161221-114630868", id = "record", issn = "1463-9971", doi = "10.4171/IFB/362", volume = "18" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160715-165131732, title = "Long-Time Asymptotics of the Filtering Distribution for Partially Observed Chaotic Dynamical Systems", journal = "SIAM/ASA Journal on Uncertainty Quantification", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160715-165131732", id = "record", issn = "2166-2525", doi = "10.1137/140997336", volume = "3" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160715-172126693, title = "Sequential Monte Carlo methods for Bayesian elliptic inverse problems", journal = "Statistics and Computing", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160715-172126693", id = "record", issn = "1573-1375", doi = "10.1007/s11222-015-9556-7", volume = "25" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160715-172927058, title = "A Multiscale Analysis of Diffusions on Rapidly Varying Surfaces", journal = "Journal of Nonlinear Science", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160715-172927058", id = "record", issn = "0938-8974", doi = "10.1007/s00332-015-9237-x", volume = "25" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160715-163821138, title = "Algorithms for Kullback--Leibler Approximation of Probability Measures in Infinite Dimensions", journal = "SIAM Journal on Scientific Computing", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160715-163821138", id = "record", issn = "1064-8275", doi = "10.1137/14098171X", volume = "37" } @book{https://resolver.caltech.edu/CaltechAUTHORS:20161110-161028249, title = "Data Assimilation: A Mathematical Introduction", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161110-161028249", id = "record", isbn = "978-3-319-20325-6", doi = "10.1007/978-3-319-20325-6" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160715-170335769, title = "Kullback-Leibler approximation for probability measures on infinite dimensional spaces", journal = "SIAM Journal on Mathematical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160715-170335769", id = "record", issn = "0036-1410", doi = "10.1137/140962802", volume = "47" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161111-104214792, title = "Data Assimilation: New Challenges in Random and Stochastic Dynamical Systems", journal = "SIAM News", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161111-104214792", id = "record", issn = "1557-9573", volume = "48" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160719-144104557, title = "Spectral gaps for a Metropolis–Hastings algorithm in infinite dimensions", journal = "Annals of Applied Probability", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160719-144104557", id = "record", issn = "1050-5164", doi = "10.1214/13-AAP982", volume = "24" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160719-114834043, title = "Well-posed Bayesian geometric inverse problems arising in subsurface flow", journal = "Inverse Problems", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160719-114834043", id = "record", issn = "0266-5611", doi = "10.1088/0266-5611/30/11/114001", volume = "30" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160719-143029648, title = "Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time", journal = "Nonlinearity", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160719-143029648", id = "record", issn = "0951-7715", doi = "10.1088/0951-7715/27/10/2579", volume = "27" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160719-141859444, title = "Analysis of the Gibbs Sampler for Hierarchical Inverse Problems", journal = "SIAM/ASA Journal on Uncertainty Quantification", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160719-141859444", id = "record", issn = "2166-2525", doi = "10.1137/130944229", volume = "2" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160719-150657732, title = "Determining white noise forcing from Eulerian observations in the Navier-Stokes equation", journal = "Stochastic Partial Differential Equations: Analysis and Computations", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160719-150657732", id = "record", issn = "2194-041X", doi = "10.1007/s40072-014-0028-4", volume = "2" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160719-145056000, title = "Noisy gradient flow from a random walk in Hilbert space", journal = "Stochastic Partial Differential Equations: Analysis and Computations", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160719-145056000", id = "record", issn = "2194-041X", doi = "10.1007/s40072-014-0029-3", volume = "2" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160719-151308932, title = "Bayesian posterior contraction rates for linear severely ill-posed inverse problems", journal = "Journal of Inverse and Ill-posed Problems", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160719-151308932", id = "record", issn = "1569-3945", doi = "10.1515/jip-2012-0071", volume = "22" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160719-152032603, title = "Analysis of the 3DVAR filter for the partially observed Lorenz'63 model", journal = "Discrete and Continuous Dynamical Systems A", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160719-152032603", id = "record", issn = "1553-5231", doi = "10.3934/dcds.2014.34.1061", volume = "34" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161111-105218524, title = "Inverse Problems and Uncertainty Quantification", journal = "SIAM News", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161111-105218524", id = "record", issn = "1557-9573" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160726-155502558, title = "Optimal tuning of the hybrid Monte Carlo algorithm", journal = "Bernoulli", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160726-155502558", id = "record", issn = "1350-7265", doi = "10.3150/12-BEJ414", volume = "19" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160727-163931558, title = "Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems", journal = "Stochastic Processes and their Applications", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160727-163931558", id = "record", issn = "0304-4149", doi = "10.1016/j.spa.2013.05.001", volume = "123" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160727-154930631, title = "MAP estimators and their consistency in Bayesian nonparametric inverse problems", journal = "Inverse Problems", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160727-154930631", id = "record", issn = "0266-5611", doi = "10.1088/0266-5611/29/9/095017", volume = "29" } 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issn = "0167-2789", doi = "10.1016/j.physd.2012.11.005", volume = "245" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160727-175235615, title = "Posterior consistency via precision operators for Bayesian nonparametric drift estimation in SDEs", journal = "Stochastic Processes and their Applications", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160727-175235615", id = "record", issn = "0304-4149", doi = "10.1016/j.spa.2012.08.010", volume = "123" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160728-150141693, title = "Optimal scaling and diffusion limits for the Langevin algorithm in high dimensions", journal = "Annals of Applied Probability", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160728-150141693", id = "record", issn = "1050-5164", doi = "10.1214/11-AAP828", volume = "22" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160728-150615482, title = "Evaluating Data Assimilation Algorithms", journal = "Monthly Weather Review", url = 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Imaging", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160728-153255881", id = "record", issn = "1930-8345", doi = "10.3934/ipi.2012.6.183", volume = "6" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160728-155039916, title = "Sparse determinisitc approximation of Bayesian inverse problems", journal = "Inverse Problems", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160728-155039916", id = "record", issn = "0266-5611", doi = "10.1088/0266-5611/28/4/045003", volume = "28" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160728-155454420, title = "Γ-Limit for Transition Paths of Maximal Probability", journal = "Journal of Statistical Physics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160728-155454420", id = "record", issn = "0022-4715", doi = "10.1007/s10955-012-0443-8", volume = "146" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160728-160352524, title = "Variational data assimilation using targetted random walks", journal = 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title = "Hybrid Monte Carlo on Hilbert spaces", journal = "Stochastic Processes and their Applications", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160804-150437807", id = "record", issn = "0304-4149", doi = "10.1016/j.spa.2011.06.003", volume = "121" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160801-175538072, title = "Kalman filtering and smoothing for linear wave equations with model error", journal = "Inverse Problems", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160801-175538072", id = "record", issn = "0266-5611", doi = "10.1088/0266-5611/27/9/095008", volume = "27" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160804-164518594, title = "A note on diffusion limits of chaotic skew-product flows", journal = "Nonlinearity", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160804-164518594", id = "record", issn = "0951-7715", doi = "10.1088/0951-7715/24/4/018", volume = "24" } 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"10.1007/978-3-642-22061-6\_1" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-075052519, title = "Random-weight particle filtering of continuous time processes", journal = "Journal of the Royal Statistical Society: Series B", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-075052519", id = "record", issn = "1369-7412", doi = "10.1111/j.1467-9868.2010.00744.x", volume = "72" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160804-164847166, title = "Random-weight particle filtering of continuous time processes", journal = "Statistical Methodology", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160804-164847166", id = "record", issn = "1467-9868", doi = "10.1111/j.1467-9868.2010.00744.x", volume = "72" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161108-161530502, title = "Transition paths in molecules at finite temperature", journal = "Journal of Chemical Physics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161108-161530502", id = "record", issn = "0021-9606", doi = "10.1063/1.3391160", volume = "132" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160804-165401982, title = "Convergence of numerical time-averaging and stationary measures via Poisson equations", journal = "SIAM Journal of Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160804-165401982", id = "record", issn = "0036-1429", doi = "10.1137/090770527", volume = "48" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161111-112136150, title = "Inverse problems: A Bayesian perspective", journal = "Acta Numerica", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161111-112136150", id = "record", issn = "0962-4929", doi = "10.1017/S0962492910000061", volume = "19" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160804-170531840, title = "Approximation of Bayesian Inverse Problems for PDEs", journal = "SIAM Journal on Numerical 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= "Stochastic Processes and their Applications", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160805-153633492", id = "record", issn = "0304-4149", doi = "10.1016/j.spa.2009.05.003", volume = "119" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170612-093904953, title = "Sixth International Congress on Industrial and Applied Mathematics", chapter = "MCMC methods for sampling function space", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-093904953", id = "record", isbn = "978-3-03719-056-2", doi = "10.4171/056-1/16" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160805-153017689, title = "Optimal scalings for local Metropolis–Hastings chains on nonproduct targets in high dimensions", journal = "Annals of Applied Probability", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160805-153017689", id = "record", issn = "1050-5164", doi = "10.1214/08-AAP563", volume = "19" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170614-080019284, title = "Trends in Stochastic Analysis", chapter = "Sampling conditioned diffusions", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170614-080019284", id = "record", isbn = "9781139107020", doi = "10.1017/CBO9781139107020.009" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160805-155749338, title = "Calculating effective diffusivities in the limit of vanishing molecular diffusion", journal = "Journal of Computational Physics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160805-155749338", id = "record", issn = "0021-9991", doi = "10.1016/j.jcp.2008.10.014", volume = "288" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160805-155341773, title = "Parameter estimation for partially observed hypoelliptic diffusions", journal = "Statistical Methodology", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160805-155341773", id = "record", issn = "1467-9868", doi = "10.1111/j.1467-9868.2008.00689.x", volume = "71" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161108-165631300, title = "Parameter estimation for partially observed hypo-elliptic diffusions", journal = "Journal of the Royal Society: Series B (Statistical Methodology)", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161108-165631300", id = "record", issn = "1467-9868", doi = "10.1111/j.1467-9868.2008.00689.x", volume = "71" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20161111-113156226, title = "Monte Carlo and Quasi-Monte Carlo Methods 2008", chapter = "Green's Functions by Monte Carlo", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161111-113156226", id = "record", isbn = "978-3-642-04106-8", doi = "10.1007/978-3-642-04107-5\_41" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170612-102025036, title = "Monte Carlo and Quasi-Monte Carlo Methods 2008", chapter = "Computational Complexity of Metropolis-Hastings Methods in High Dimensions", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-102025036", id = "record", isbn = "978-3-642-04106-8", doi = "10.1007/978-3-642-04107-5\_4" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160805-165106874, title = "MCMC Methods for Diffusion Bridges", journal = "Stochastics and Dynamics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160805-165106874", id = "record", issn = "1793-6799", doi = "10.1142/S0219493708002378", volume = "8" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20160805-165730529, title = "Data assimilation: Mathematical and statistical perspectives", journal = "International Journal for Numerical Methods in Fluids", url = "https://resolver.caltech.edu/CaltechAUTHORS:20160805-165730529", id = "record", issn = "0271-2091", doi = "10.1002/fld.1698", volume = "56" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161108-173409695, title = "A Bayesian approach to Lagrangian data assimilation", journal = "Tellus A", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161108-173409695", id = "record", issn = "0280-6495", doi = "10.1111/j.1600-0870.2007.00295.x", volume = "60" } @book{https://resolver.caltech.edu/CaltechAUTHORS:20161110-163303162, title = "A First Course in Continuum Mechanics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161110-163303162", id = "record", isbn = "9780521714242", doi = "10.1017/CBO9780511619571" } @book{https://resolver.caltech.edu/CaltechAUTHORS:20161110-162102417, title = "Multiscale Methods: Averaging and Homogenization", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161110-162102417", id = "record", isbn = "978-0-387-73829-1", doi = "10.1007/978-0-387-73829-1" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-132345468, title = "An adaptive Euler-Maruyama scheme for SDEs: convergence and stability", journal = "IMA Journal of Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-132345468", id = "record", issn = "0272-4979", doi = "10.1093/imanum/drl032", volume = "27" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-130839195, title = "Sampling the posterior: An approach to non-Gaussian data assimilation", journal = "Physica D", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-130839195", id = "record", issn = "0167-2789", doi = "10.1016/j.physd.2006.06.009", volume = "230" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-124705885, title = "Parameter Estimation for Multiscale Diffusions", journal = "Journal of Statistical Physics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-124705885", id = "record", issn = "0022-4715", doi = "10.1007/s10955-007-9300-6", volume = "127" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20161108-174342361, title = "Homogenization for inertial particles in a random flow", journal = "Communications in Mathematical Sciences", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161108-174342361", id = "record", issn = "1539-6746", doi = "10.4310/CMS.2007.v5.n3.a1", volume = "5" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-080132206, title = "Analysis of SPDEs arising in path sampling part II: The nonlinear case", journal = "Annals of Applied Probability", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-080132206", id = "record", issn = "1050-5164", doi = "10.1214/07-AAP441", volume = "17" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-131025773, title = "The Moment Map: Nonlinear Dynamics of Density Evolution via a Few Moments", journal = "SIAM Journal on Applied Dynamical Systems", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-131025773", id = "record", issn = "1536-0040", doi = "10.1137/050638667", volume = "5" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170613-140425580, title = "Monte Carlo and Quasi-Monte Carlo Methods 2004", chapter = "Monte Carlo Studies of Effective Diffusivities for Inertial Particles", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-140425580", id = "record", isbn = "978-3-540-25541-3", doi = "10.1007/3-540-31186-6\_26" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-130002475, title = "Analysis of White Noise Limits for Stochastic Systems with Two Fast Relaxation Times", journal = "Multiscale Modeling and Simulation", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-130002475", id = "record", issn = "1540-3459", doi = "10.1137/040610507", volume = "4" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-143518545, title = "Periodic homogenization for inertial particles", journal = "Physica D", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-143518545", id = "record", issn = "0167-2789", doi = "10.1016/j.physd.2005.04.011", volume = "204" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-141658808, title = "Analysis of SPDEs arising in path sampling. Part I: The Gaussian case", journal = "Communications in Mathematical Sciences", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-141658808", id = "record", issn = "1539-6746", doi = "10.4310/CMS.2005.v3.n4.a8", volume = "3" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-143006730, title = "Fitting SDE models to nonlinear Kac–Zwanzig heat bath models", journal = "Physica D", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-143006730", id = "record", issn = "0167-2789", doi = "10.1016/j.physd.2004.04.011", volume = "199" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-144819276, title = "Conditional Path Sampling of SDEs and the Langevin MCMC Method", journal = "Communications in Mathematical Sciences", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-144819276", id = "record", issn = "1539-6746", doi = "10.4310/CMS.2004.v2.n4.a7", volume = "2" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-153344149, title = "Extracting macroscopic dynamics: model problems and algorithms", journal = "Nonlinearity", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-153344149", id = "record", issn = "0951-7715", doi = "10.1088/0951-7715/17/6/R01", volume = "17" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-132002885, title = "Itô versus Stratonovich white-noise limits for systems with inertia and colored multiplicative noise", journal = "Physical Review E", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-132002885", id = "record", issn = "1539-3755", doi = "10.1103/PhysRevE.70.036120", volume = "70" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-165633126, title = "White Noise Limits for Inertial Particles in a Random Field", journal = "Multiscale Modeling and Simulation", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-165633126", id = "record", issn = "1540-3459", doi = "10.1137/S1540345903421076", volume = "1" } 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Differential Equations", journal = "SIAM Journal on Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-133526351", id = "record", issn = "0036-1429", doi = "10.1137/S0036142901389530", volume = "40" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-164822143, title = "The dynamical behavior of the discontinuous Galerkin method and related difference schemes", journal = "Mathematics of Computation", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-164822143", id = "record", issn = "0025-5718", doi = "10.1090/S0025-5718-01-01364-3", volume = "71" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-073927763, title = "Inertial Particles in a Random Field", journal = "Stochastics and Dynamics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-073927763", id = "record", issn = "1793-6799", doi = "10.1142/S021949370200042X", volume = "02" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-125012320, title = "Geometric Ergodicity of Some Hypo-Elliptic Diffusions for Particle Motions", journal = "Markov Processes And Related Fields", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-125012320", id = "record", issn = "1024-2953", volume = "8" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170613-125750895, title = "Modern Methods in Scientific Computing and Applications", chapter = "Deterministic and random dynamical systems: theory and numerics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-125750895", id = "record", isbn = "978-1-4020-0782-8", doi = "10.1007/978-94-010-0510-4\_6" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-063817274, title = "Algorithms for Particle-Field Simulations with Collisions", journal = "Journal of Computational Physics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-063817274", id = "record", issn = "0021-9991", doi = "10.1006/jcph.2001.6858", volume = "172" } 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@article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-080747440, title = "A Perturbation Theory for Ergodic Markov Chains and Application to Numerical Approximations", journal = "SIAM Journal on Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-080747440", id = "record", issn = "0036-1429", doi = "10.1137/S0036142998337235", volume = "37" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170613-142949630, title = "Dynamics of Algorithms", chapter = "Convergence Proofs for Numerical IVP Software", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-142949630", id = "record", isbn = "9781461270737", doi = "10.1007/978-1-4612-1274-4\_6" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-161129844, title = "Analysis and Experiments for a Computational Model of a Heat Bath", journal = "Journal of Statistical Physics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-161129844", id = "record", issn = "0022-4715", doi = "10.1023/A:1004667325896", volume = "97" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-124028394, title = "Ergodicity of Dissipative Differential Equations Subject to Random Impulses", journal = "Journal of Differential Equations", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-124028394", id = "record", issn = "0022-0396", doi = "10.1006/jdeq.1998.3594", volume = "155" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-164025962, title = "Qualitative properties of modified equations", journal = "IMA Journal of Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-164025962", id = "record", issn = "0272-4979", doi = "10.1093/imanum/19.2.169", volume = "19" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-154149149, title = "Convergence results for the MATLAB ODE23 routine", journal = "BIT Numerical Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-154149149", id = "record", issn = "0006-3835", doi = "10.1007/BF02510413", volume = "38" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-134545090, title = "Space-Time Continuous Analysis of Waveform Relaxation for the Heat Equation", journal = "SIAM Journal on Scientific Computing", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-134545090", id = "record", issn = "1064-8275", doi = "10.1137/S1064827596305337", volume = "19" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-143618623, title = "On the Solution of Convection-Diffusion Boundary Value Problems Using Equidistributed Grids", journal = "SIAM Journal on Scientific Computing", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-143618623", id = "record", issn = "1064-8275", doi = "10.1137/S1064827595280454", volume = "20" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-123316540, title = "Persistence of Invariant Sets for Dissipative Evolution Equations", journal = "Journal of Mathematical Analysis and Applictions", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-123316540", id = "record", issn = "0022-247X", doi = "10.1006/jmaa.1997.5847", volume = "219" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-110046810, title = "Analysis of the dynamics of local error control via a piecewise continuous residual", journal = "BIT Numerical Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-110046810", id = "record", issn = "0006-3835", doi = "10.1007/BF02510916", volume = "38" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-145717225, title = "Waveform relaxation as a dynamical system", journal = "Mathematics of Computation", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-145717225", id = "record", issn = "0025-5718", doi = "10.1090/S0025-5718-97-00847-8", volume = "66" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-132616648, title = "Probabilistic and deterministic convergence proofs for software for initial value problems", journal = "Numerical Algorithms", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-132616648", id = "record", issn = "1017-1398", doi = "10.1023/A:1019169114976", volume = "14" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170613-141546199, title = "The State of the Art in Numerical Analysis", chapter = "Convergence and stability in the numerical approximation of dynamical systems", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-141546199", id = "record", isbn = "9780198500148" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-125856997, title = "Viscous Cahn–Hilliard Equation II. Analysis", journal = "Journal of Differential Equations", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-125856997", id = "record", issn = "0022-0396", doi = "10.1006/jdeq.1996.0101", volume = "128" } @book{https://resolver.caltech.edu/CaltechAUTHORS:20161110-163922626, title = "Dynamical Systems and Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20161110-163922626", id = "record", isbn = "9780521645638" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-084044146, title = "The Essential Stability of Local Error Control for Dynamical Systems", journal = "SIAM Journal on Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-084044146", id = "record", issn = "0036-1429", doi = "10.1137/0732087", volume = "32" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-064633625, title = "Attractive Invariant Manifolds under Approximation. Inertial Manifolds", journal = "Journal of Differential Equations", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-064633625", id = "record", issn = "0022-0396", doi = "10.1006/jdeq.1995.1174", volume = "123" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-104839336, title = "The rate of error growth in Hamiltonian-conserving integrators", journal = "Zeitschrift für Angewandte Mathematik und Physik", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-104839336", id = "record", issn = "0044-2275", doi = "10.1007/BF01003559", volume = "46" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-143108777, title = "Discrete Gevrey regularity attractors and uppers–semicontinuity for a finite difference approximation to the Ginzburg–Landau equation", journal = "Numerical Functional Analysis and Optimization", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-143108777", id = "record", issn = "0163-0563", doi = "10.1080/01630569508816658", volume = "16" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-135245414, title = "The viscous Cahn-Hilliard equation. I. Computations", journal = "Nonlinearity", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-135245414", id = "record", issn = "0951-7715", doi = "10.1088/0951-7715/8/2/002", volume = "8" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170613-133150018, title = "Theory and Numerics of Ordinary and Partial Differential Equations", chapter = "Perturbation Theory for Infinite Dimensional Dynamical Systems", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-133150018", id = "record", isbn = "978-0198511939" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170609-122809369, title = "Numerical computations of coarsening in the one-dimensional Cahn-Hilliard model of phase separation", journal = "Physica D", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170609-122809369", id = "record", issn = "0167-2789", doi = "10.1016/0167-2789(94)90112-0", volume = "78" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-084043889, title = "Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems", journal = "SIAM Journal on Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-084043889", id = "record", issn = "0036-1429", doi = "10.1137/0731075", volume = "31" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-120606856, title = "Blow-up in a System of Partial Differential Equations with Conserved First Integral. Part II: Problems with Convection", journal = "SIAM Journal on Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-120606856", id = "record", issn = "0036-1399", doi = "10.1137/S0036139992232131", volume = "54" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-100013806, title = "Model Problems in Numerical Stability Theory for Initial Value Problems", journal = "SIAM Review", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-100013806", id = "record", issn = "0036-1445", doi = "10.1137/1036054", volume = "36" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170612-152618052, title = "Numerical Analysis 1993", chapter = "Approximation of dissipative partial differential equations over long time intervals", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-152618052", id = "record", isbn = "9780582225688" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-082428693, title = "Numerical analysis of dynamical systems", journal = "Acta Numerica", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-082428693", id = "record", issn = "0962-4929", doi = "10.1017/S0962492900002488", volume = "3" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-070150162, title = "The Global Dynamics of Discrete Semilinear Parabolic Equations", journal = "SIAM Journal on Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-070150162", id = "record", issn = "0036-1429", doi = "10.1137/0730084", volume = "30" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-071258761, title = "A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor", journal = "Mathematical Medicine and Biology", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-071258761", id = "record", issn = "1477-8599", doi = "10.1093/imammb/10.3.149", volume = "10" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-080915743, title = "Blowup in a Partial Differential Equation with Conserved First Integral", journal = "SIAM Journal on Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-080915743", id = "record", issn = "0036-1399", doi = "10.1137/0153036", volume = "53" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-082542564, title = "The Numerical Computation of Heteroclinic Connections in Systems of Gradient Partial Differential Equations", journal = "SIAM Journal on Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-082542564", id = "record", issn = "0036-1399", doi = "10.1137/0153037", volume = "53" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-105155948, title = "Unified approach to spurious solutions introduced by time discretization Part II: BDF-like methods", journal = "IMA Journal of Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-105155948", id = "record", issn = "0272-4979", doi = "10.1093/imanum/12.4.487", volume = "12" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-084043611, title = "Numerical Wave Propagation in an Advection Equation with a Nonlinear Source Term", journal = "SIAM Journal on Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-084043611", id = "record", issn = "0036-1429", doi = "10.1137/0729074", volume = "29" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-070148270, title = "A note on uniform in time error estimates for approximations to reaction-diffusion equations", journal = "IMA Journal of Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-070148270", id = "record", issn = "0272-4979", doi = "10.1093/imanum/12.3.457", volume = "12" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-164247464, title = "A Unified Approach to Spurious Solutions Introduced by Time Discretisation. Part I: Basic Theory", journal = "SIAM Journal on Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-164247464", id = "record", issn = "0036-1429", doi = "10.1137/0728086", volume = "28" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-092411747, title = "The Dynamics of the Theta Method", journal = "SIAM Journal on Scientific and Statistical Computing", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-092411747", id = "record", issn = "0196-5204", doi = "10.1137/0912074", volume = "12" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-104202241, title = "A Mathematical Model for the Diffusion of Tumour Angiogenesis Factor into the Surrounding Host Tissue", journal = "Mathematical Medicine and Biology", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-104202241", id = "record", issn = "1477-8599", doi = "10.1093/imammb/8.3.191", volume = "8" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-144801379, title = "Singular Limits in Free Boundary Problems", journal = "Rocky Mountain Journal of Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-144801379", id = "record", issn = "0035-7596", doi = "10.1216/rmjm/1181072969", volume = "21" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-101245620, title = "On the computation of blow-up", journal = "European Journal of Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-101245620", id = "record", issn = "0956-7925", doi = "10.1017/S095679250000005X", volume = "1" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170612-140046210, title = "Continuation and Bifurcations: Numerical Techniques and Applications", chapter = "The Global Attractor Under Discretisation", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-140046210", id = "record", isbn = "978-94-010-6781-2", doi = "10.1007/978-94-009-0659-4\_14" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-083455306, title = "Linear Instability Implies Spurious Periodic Solutions", journal = "IMA Journal of Numerical Analysis", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-083455306", id = "record", issn = "0272-4979", doi = "10.1093/imanum/9.4.465", volume = "9" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-075253765, title = "Nonlinear Instability in Dissipative Finite Difference Schemes", journal = "SIAM Review", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-075253765", id = "record", issn = "0036-1445", doi = "10.1137/1031048", volume = "31" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-090547094, title = "A Model for Porous-Medium Combustion", journal = "Quarterly Journal of Mechanics and Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-090547094", id = "record", issn = "0033-5614", doi = "10.1093/qjmam/42.1.159", volume = "42" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-080915333, title = "Singular Free Boundary Problems and Local Bifurcation Theory", journal = "SIAM Journal on Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-080915333", id = "record", issn = "0036-1399", doi = "10.1137/0149004", volume = "49" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-135127282, title = "A Note on High/Low-Wave-Number Interactions in Spatially Discrete Parabolic Equations", journal = "IMA Journal of Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-135127282", id = "record", issn = "0272-4960", doi = "10.1093/imamat/42.1.27", volume = "42" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-090149803, title = "Similarity Solutions of a Heat Equation with Nonlinearly Varying Heat Capacity", journal = "IMA Journal of Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-090149803", id = "record", issn = "0272-4960", doi = "10.1093/imamat/40.3.217", volume = "40" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-164819129, title = "Travelling Combustion Waves in a Porous Medium. Part II—Stability", journal = "SIAM Journal on Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-164819129", id = "record", issn = "0036-1399", doi = "10.1137/0148019", volume = "48" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-165322289, title = "Travelling Combustion Waves in a Porous Medium. Part I—Existence", journal = "SIAM Journal on Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-165322289", id = "record", issn = "0036-1399", doi = "10.1137/0148007", volume = "48" } @inbook{https://resolver.caltech.edu/CaltechAUTHORS:20170612-132031395, title = "Nonlinear Diffusion Equations and Their Equilibrium States II", chapter = "The Mathematics of Porous Medium Combustion", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-132031395", id = "record", isbn = "978-1-4613-9610-9", doi = "10.1007/978-1-4613-9608-6\_18" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170613-084535886, title = "Parabolic Free Boundary Problems Arising in Porous Medium Combustion", journal = "IMA Journal of Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170613-084535886", id = "record", issn = "0272-4960", doi = "10.1093/imamat/39.3.241", volume = "39" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-142648576, title = "Existence of Solutions of a Two-Point Free-Boundary Problem Arising in the Theory of Porous Medium Combustion", journal = "IMA Journal of Applied Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-142648576", id = "record", issn = "0272-4960", doi = "10.1093/imamat/38.1.23", volume = "38" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-135043115, title = "Volterra integral equations and a new Gronwall inequality (Part II: The nonlinear case)", journal = "Proceedings of the Royal Society of Edinburgh: Section A Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-135043115", id = "record", issn = "0308-2105", doi = "10.1017/S0308210500018485", volume = "106" } @article{https://resolver.caltech.edu/CaltechAUTHORS:20170612-131130001, title = "Volterra integral equations and a new Gronwall inequality (Part I: The linear case)", journal = "Proceedings of the Royal Society of Edinburgh: Section A Mathematics", url = "https://resolver.caltech.edu/CaltechAUTHORS:20170612-131130001", id = "record", issn = "0308-2105", doi = "10.1017/S0308210500018473", volume = "106" }