Smooth solution for the porous medium equation in a bounded domain

DOI10.1016/j.jde.2009.05.001zbMath1180.35308OpenAlexW2061383526WikidataQ125291637 ScholiaQ125291637MaRDI QIDQ1029147

Ki-Ahm Lee, Sung Hoon Kim

Publication date: 9 July 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.05.001

zbMATH Keywords

existencecoercive estimateweighted Hölder space

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Degenerate parabolic equations (35K65) Quasilinear parabolic equations (35K59)

Related Items (12)

Hölder regularity and uniqueness theorem on weak solutions to the degenerate Keller-Segel system ⋮ Initial-boundary value problem for a fractional type degenerate heat equation ⋮ Power concavity in weakly coupled elliptic and parabolic systems ⋮ Optimal regularity and fine asymptotics for the porous medium equation in bounded domains ⋮ System of porous medium equations ⋮ Singular limits and properties of solutions of some degenerate elliptic and parabolic equations ⋮ Parabolic power concavity and parabolic boundary value problems ⋮ Local continuity and asymptotic behaviour of degenerate parabolic systems ⋮ Classical solvability of the multidimensional free boundary problem for the thin film equation with quadratic mobility in the case of partial wetting ⋮ Long time existence of smooth solution for the porous medium equation in a bounded domain ⋮ Classical solvability of multidimensional two-phase Stefan problem for degenerate parabolic equations and Schauder's estimates for a degenerate parabolic problem with dynamic boundary conditions ⋮ Higher regularity up to boundary for degenerate parabolic equations

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• Regularity of the free boundary for the porous medium equation
• The free boundary in the Gauss Curvature Flow with flat sides
• ON THE CLASSICAL SOLUTION OF NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER

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