Cauchy-Dirichlet problems for the porous medium equation

DOI10.3934/dcds.2022182zbMath1523.35211OpenAlexW4312925614MaRDI QIDQ6160083

John R. King, Mark Bowen, Thomas P. Witelski

Publication date: 23 June 2023

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2022182

zbMATH Keywords

Dirichlet problemporous medium equationsimilarity solutionsconserved quantitiesnonlinear diffusion

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order parabolic equations (35K20) Degenerate parabolic equations (35K65) Free boundary problems for PDEs (35R35) Quasilinear parabolic equations (35K59)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the large-time asymptotics of the diffusion equation on infinite domains
• Asymptotic analysis of extinction behaviour in fast nonlinear diffusion
• Perturbation methods in applied mathematics
• Large time behaviour of solutions of the porous medium equation in bounded domains
• Integral results for nonlinear diffusion equations
• Explicit solutions of a two-dimensional fourth-order nonlinear diffusion equation
• ADI schemes for higher-order nonlinear diffusion equations.
• Non-uniqueness of solutions of nonlinear heat equations of fast diffusion type
• The porous media equation in an infinite cylinder, between two infinite parallel plates, and like spatial domains
• “Waiting-time” Solutions of a Nonlinear Diffusion Equation
• The Asymptotic Behavior of Gas in an n-Dimensional Porous Medium
• Waiting-Time Behavior in a Nonlinear Diffusion Equation
• Asymptotic Behaviour of Solutions of the Porous Medium Equation with Changing Sign
• EXACT MULTIDIMENSIONAL SOLUTIONS TO SOME NONLINEAR DIFFUSION EQUATIONS
• Self-similar behaviour for the equation of fast nonlinear diffusion
• Self‐similar Asymptotics for Linear and Nonlinear Diffusion Equations
• POROUS MEDIUM FLOW IN A TUBE: TRAVELING WAVES AND KPP BEHAVIOR
• DIFFUSION FROM AN INSTANTANEOUS POINT SOURCE WITH A CONCENTRATION-DEPENDENT COEFFICIENT
• Similarity solutions of the porous medium equation with sign changes
• Focusing of an elongated hole in porous medium flow
• Intermediate asymptotics of the porous medium equation with sign changes

This page was built for publication: Cauchy-Dirichlet problems for the porous medium equation