Regularity of solutions and interfaces of the porous medium equation via local estimates

DOI10.1017/S0308210500028146zbMath0692.35025OpenAlexW2131479207MaRDI QIDQ3034143

Juan Luis Vazquez

Publication date: 1989

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500028146

zbMATH Keywords

interfacesporous medium equationlocal a priori estimates\(C^{\infty }\) regularity

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Flows in porous media; filtration; seepage (76S05) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45)

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Cites Work

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• \(C^{\infty}\)-regularity for the porous medium equation
• Eventual \(C^{\infty}\)-regularity and concavity for flows in one- dimensional porous media
• Large time behaviour of solutions of the porous medium equation in bounded domains
• Regularity properties of flows through porous media: The interface
• The Interfaces of One-Dimensional Flows in Porous Media
• Asymptotic Behaviour and Propagation Properties of the One-Dimensional Flow of Gas in a Porous Medium
• “Waiting-time” Solutions of a Nonlinear Diffusion Equation
• How an Initially Stationary Interface Begins to Move in Porous Medium Flow
• Interfaces with a corner point in one-dimensional porous medium flow
• Non-negative solutions of theo porous medium eqation
• Stabilization of solutions of a degenerate nonlinear diffusion problem
• Concavity of Solutions of the Porous Medium Equation
• The One-Dimensional Nonlinear Heat Equation with Absorption: Regularity of Solutions and Interfaces
• Regularity of the Free Boundary for the One-Dimensional Flow of Gas in a Porous Medium
• Regularity Propeties of Flows Through Porous Media
• Regularity Properties of Flows Through Porous Media: A Counterexample