A singular limit problem for the porous medium equation

DOI10.1016/0022-247X(89)90077-2zbMath0688.35035OpenAlexW1979115093MaRDI QIDQ1263734

Paul E. Sacks

Publication date: 1989

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(89)90077-2

zbMATH Keywords

convergencelimit problemsemigroup solutionparameter dependent solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Flows in porous media; filtration; seepage (76S05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items

Asymptotic behavior of the solutions of the \(p\)-Laplacian equation, Singular limit of solutions of the generalized p-Laplacian equation, Singular limit of the generalized Burgers equation with absorption, Limiting behavior of solutions of \(u_ t=\Delta{} u^ m\;as\;m\rightarrow{} \infty\), The Hele-Shaw asymptotics for mechanical models of tumor growth, Singular limit of solutions of the very fast diffusion equation, Singular limit of solutions of the \(p\)-Laplacian equation, Corrections to: ``Limiting behavior of solutions of \(u_ t={\Delta{}}u^ m\) as \(m{\to{}}\infty{}\), Obstructions to existence in fast-diffusion equations, Convergence of the porous media equation to Hele-Shaw, Singular limit of solutions of the porous medium equation with absorption, Boundary layer formation in the transition from the porous media equation to a Hele-Shaw flow.

Cites Work

• On the Mesa problem
• Some \(L^ 1\) existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions
• Semi-linear second-order elliptic equations in \(L^1\)
• The Mesa Problem: Diffusion Patterns for u_t = ∇ · (u^m∇u) as m → +∞
• Continuity of the Density of a Gas Flow in a Porous Medium
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