\(C^{\infty}\)-regularity for the porous medium equation

DOI10.1007/BF01179424zbMath0597.35107OpenAlexW2093764695MaRDI QIDQ1078768

Klaus Höllig, Heinz-Otto Kreiss

Publication date: 1986

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173730

zbMATH Keywords

weak solutionporous medium equationfree boundariesregularity result

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Flows in porous media; filtration; seepage (76S05) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

Local existence and regularity for a class of degenerate parabolic equations, Eventual \(C^{\infty}\)-regularity and concavity for flows in one- dimensional porous media, The occurrence of interfaces in nonlinear diffusion-advection processes, Optimal regularity and fine asymptotics for the porous medium equation in bounded domains, The interface between regions where u<0 andu > 0in the porous medium equation, Regularity of solutions and interfaces of the porous medium equation via local estimates, How parabolic free boundaries approximate hyperbolic fronts, Analyticity of the Interface of the Porous Media Equation After the Waiting Time, Free boundary regularity of the porous medium equation with nonlocal drifts in dimension one, Regularity of the free boundary for the porous medium equation

Cites Work

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• Asymptotic Behaviour and Propagation Properties of the One-Dimensional Flow of Gas in a Porous Medium
• A coordinate transformation for the porous media equation that renders the free boundary stationary
• Regularity of the Free Boundary for the One-Dimensional Flow of Gas in a Porous Medium
• The Porous Medium Equation in One Dimension
• Regularity Properties of Flows Through Porous Media: A Counterexample