Regularity Propeties of Flows Through Porous Media 论文

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Previous article Next article Regularity Propeties of Flows Through Porous MediaD. G. AronsonD. G. Aronsonhttps://doi.org/10.1137/0117045PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] M. Muskat, The Flow of Homogeneous Fluids Through Porous Media, McGraw-Hill, New York, 1937 Google Scholar[2] Olga Olei˘nik, On some degenerate quasilinear parabolic equations, Seminari 1962/63 Anal. Alg. Geom. e Topol., Vol. 1, Ist. Naz. Alta Mat., Ediz. Cremonese, Rome, 1965, 355–371 MR0192205 Google Scholar[3] O. A. Oleinik and , S. N. Kruzhkov, Quasi-linear second-order parabolic equations with many independent variables, Russian Math. Surveys, 16 (1961), 106–146 10.1070/rm1961v016n05ABEH004114 0112.32604 CrossrefGoogle Scholar[4] O. A. Oleinik, , A. S. Kalashinkov and , Yui-Lin' Chzhou, The Cauchy problem and boundary problems for equations of the type of non-stationary filtration, Izv. Akad. Nauk SSSR. Ser. Mat., 22 (1958), 667–704 MR0099834 Google Scholar[5] R. E. Pattle, Diffusion from an instantaneous point source with a concentration-dependent coefficient, Quart. J. Mech. Appl. Math., 12 (1959), 407–409 MR0114505 0119.30505 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Improved regularity for the porous medium equation along zero level sets6 October 2021 | Israel Journal of Mathematics, Vol. 245, No. 1 Cross Ref Pointwise Gradient Estimates in Multi-dimensional Slow Diffusion Equations with a Singular Quenching Term19 March 2020 | Advanced Nonlinear Studies, Vol. 20, No. 2 Cross Ref A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton–Jacobi equations18 November 2019 | Communications in Partial Differential Equations, Vol. 45, No. 4 Cross Ref Hölder Regularity for Singular Parabolic Obstacle Problems of Porous Medium Type24 April 2018 | International Mathematics Research Notices, Vol. 2020, No. 6 Cross Ref Adaptive finite element solution of the porous medium equation in pressure formulation21 January 2019 | Numerical Methods for Partial Differential Equations, Vol. 35, No. 3 Cross Ref Numerical methods for porous medium equation by an energetic variational approachJournal of Computational Physics, Vol. 385 Cross Ref A Multiscale Particle Method for Mean Field Equations: The General CaseAxel Klar and Sudarshan Tiwari30 January 2019 | Multiscale Modeling & Simulation, Vol. 17, No. 1AbstractPDF (2873 KB)Inferring Filtration Laws from the Spreading of a Liquid Modelled by the Porous Medium EquationA. 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Herrero and Juan L. 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I. Weak shock waves1 January 1997 | Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, Vol. 393, No. 1805 Cross Ref Some properties of the solution of a filtration problem in partially saturated porous mediaActa Mathematicae Applicatae Sinica, Vol. 1, No. 1 Cross Ref The flow of two immiscible fluids through a porous mediumNonlinear Analysis: Theory, Methods & Applications, Vol. 8, No. 4 Cross Ref Stationary solutions of a spatially aggregating population modelProceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 60, No. 2 Cross Ref A Markov process associated with a porous medium equationProceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 60, No. 5 Cross Ref A coordinate transformation for the porous media equation that renders the free boundary stationary1 January 1984 | Quarterly of Applied Mathematics, Vol. 42, No. 3 Cross Ref An interface tracking algorithm for the porous medium equation1 January 1984 | Transactions of the American Mathematical Society, Vol. 284, No. 2 Cross Ref Behaviour of the velocity of one-dimensional flows in porous media1 January 1984 | Transactions of the American Mathematical Society, Vol. 286, No. 2 Cross Ref How an Initially Stationary Interface Begins to Move in Porous Medium FlowD. G. Aronson, L. A. Caffarelli, and S. Kamin17 July 2006 | SIAM Journal on Mathematical Analysis, Vol. 14, No. 4AbstractPDF (1453 KB)Asymptotic Behavior for a Nonlinear Degenerate Diffusion Equation in Population DynamicsToshitaka Nagai and Masayasu Mimura12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 43, No. 3AbstractPDF (1146 KB)Some questions and open problems in continuum mechanics and population dynamicsJournal of Differential Equations, Vol. 48, No. 2 Cross Ref Existence Analysis via the Stability of Consistent Semidiscrete Approximations Cross Ref Some nonlinear degenerate diffusion equations with a nonlocally convective term in ecologyHiroshima Mathematical Journal, Vol. 13, No. 1 Cross Ref Numerical approximations to interface curves for a porous media equationHiroshima Mathematical Journal, Vol. 13, No. 2 Cross Ref Numerical methods for flows through porous media. I1 January 1983 | Mathematics of Computation, Vol. 40, No. 162 Cross Ref Asymptotic behaviour and propagation properties of the one-dimensional flow of gas in a porous medium1 January 1983 | Transactions of the American Mathematical Society, Vol. 277, No. 2 Cross Ref Nonstationary filtration in partially saturated porous mediaArchive for Rational Mechanics and Analysis, Vol. 78, No. 2 Cross Ref Asymptotic Behavior of Solutions of a Nonlinear Diffusion EquationM. Bertsch12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 42, No. 1AbstractPDF (864 KB)A Nonlinear Evolution Problem Arising in the Physics of Ionized GasesD. Hilhorst17 July 2006 | SIAM Journal on Mathematical Analysis, Vol. 13, No. 1AbstractPDF (1879 KB)The existence and non-existence of global solutions of boundary value problems for quasi-linear parabolic equationsUSSR Computational Mathematics and Mathematical Physics, Vol. 22, No. 6 Cross Ref References Cross Ref On the propagation properties of a nonlinear degenerate parabolic equation8 May 2007 | Communications in Partial Differential Equations, Vol. 7, No. 12 Cross Ref Traveling Wave Solution for Some Nonlinear Diffusion EquationsC. Atkinson, G. E. H. Reuter, and C. J. Ridler-Rowe17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 12, No. 6AbstractPDF (1227 KB)Test solutions of porous media problemsJournal of Mathematical Analysis and Applications, Vol. 79, No. 1 Cross Ref Global classical solutions to ut − Δ(u2m + 1) + λu = ƒJournal of Differential Equations, Vol. 38, No. 2 Cross Ref Degenerate parabolic equations with general nonlinearitiesNonlinear Analysis: Theory, Methods & Applications, Vol. 4, No. 6 Cross Ref Evolution of a stable profile for a class of nonlinear diffusion equations. III. Slow diffusion on the lineJournal of Mathematical Physics, Vol. 21, No. 6 Cross Ref Application of recent results in functional analysis to the problem of wetting fronts9 July 2010 | Water Resources Research, Vol. 16, No. 2 Cross Ref Horizontal line analysis of the multidimensional porous medium equation: Existence, rate of convergence and maximum principles14 October 2006 Cross Ref Regularity results for the porous media equationAnnali di Matematica Pura ed Applicata, Vol. 121, No. 1 Cross Ref Regularity properties of solutions of an equation arising in the theory of turbulenceJournal of Differential Equations, Vol. 33, No. 2 Cross Ref Time Dependent Free Boundary ProblemsAvner Friedman17 February 2012 | SIAM Review, Vol. 21, No. 2AbstractPDF (849 KB)Stabilization of Flows Through Porous MediaB. H. Gilding17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 10, No. 2AbstractPDF (937 KB)The behavior of the support of solutions of the equation of nonlinear heat conduction with absorption in one dimensionTransactions of the American Mathematical Society, Vol. 249, No. 2 Cross Ref A numerical method for solving the problem $u_t - \Delta f (u) = 0$13 May 2009 | RAIRO. Analyse numérique, Vol. 13, No. 4 Cross Ref A similarity solution to a nonlinear diffusion equation of the singular type: a uniformly valid solution by perturbations1 January 1979 | Quarterly of Applied Mathematics, Vol. 37, No. 1 Cross Ref Continuity of the density of a gas flow in a porous medium1 January 1979 | Transactions of the American Mathematical Society, Vol. 252, No. 0 Cross Ref О Некоторых свойствах обобщенных решений квазилинейных вырождающихся параболических уравненийActa Mathematica Academiae Scientiarum Hungaricae, Vol. 32, No. 3-4 Cross Ref Application of Nonlinear Semigroup Theory to Certain Partial Differential Equations Cross Ref Differentiability of a nonlinear semigroup in L1Journal of Mathematical Analysis and Applications, Vol. 60, No. 3 Cross Ref Properties of solutions of an equation in the theory of infiltrationArchive for Rational Mechanics and Analysis, Vol. 65, No. 3 Cross Ref On the diffusion of biological populationsMathematical Biosciences, Vol. 33, No. 1-2 Cross Ref References Cross Ref Wave solutions travelling along quadratic paths for the equation (∂/∂)-(𝑘(𝑢)𝑢ₓ)ₓ=01 January 1977 | Quarterly of Applied Mathematics, Vol. 35, No. 1 Cross Ref The porous medium equation in one dimension1 January 1977 | Transactions of the American Mathematical Society, Vol. 234, No. 2 Cross Ref The cauchy problem for an equation in the theory of infiltrationArchive for Rational Mechanics and Analysis, Vol. 61, No. 2 Cross Ref Some estimates for solution of the Cauchy problem for equations of a nonstationary filtrationJournal of Differential Equations, Vol. 20, No. 2 Cross Ref Quasilinear parabolic systemsJournal of Differential Equations, Vol. 20, No. 2 Cross Ref References Cross Ref On the Numerical Treatment of Partial Differential Equations in the Neighborhood of Isolated Singularities with Applications Cross Ref Nonexistence theorems for the heat equation with nonlinear boundary and for the porous medium equation in of Differential Equations, Vol. 16, No. 2 Cross Ref Continuity of solutions of the cauchy problem for the porous medium equation26 August 2006 Cross Ref The propagation of in problems of heat conduction with Computational Mathematics and Mathematical Physics, Vol. 14, No. 4 Cross Ref The asymptotic behaviour of the solution of the filtration Journal of Mathematics, Vol. 14, No. 1 Cross Ref A on fluid flows through porous of the Japan Academy, Series A, Mathematical Sciences, Vol. 49, No. 1 Cross Ref solutions for degenerate quasilinear parabolic equationsJournal of Mathematical Analysis and Applications, Vol. 38, No. 1 Cross Ref Numerical solution of some degenerate parabolic Vol. 12, No. 1 Cross Ref in in Medium Cross Ref Asymptotic Behavior of Solutions of the Porous Media A. July 2006 | SIAM Journal on Applied Mathematics, Vol. 21, No. 4AbstractPDF KB)A Finite to Some Degenerate Nonlinear Parabolic L. and P. July 2006 | SIAM Journal on Applied Mathematics, Vol. 20, No. 2AbstractPDF Methods in and Some Applications to Nonlinear Partial Differential Equations Cross Ref Regularity Properties of Flows Through Porous Media: A G. February 2012 | SIAM Journal on Applied Mathematics, Vol. 19, No. 2AbstractPDF KB)Regularity properties of flows through porous The for Rational Mechanics and Analysis, Vol. 37, No. 1 Cross Ref Cross Ref the of the continuity of solutions of parabolic equations and some of their of the of of the Vol. 6, No. 1 Cross Ref 17, Journal on Applied Mathematics July July 2006 Society for and Applied & for and Applied Mathematics