Source-type solutions of the porous media equation with absorption: The fast diffusion case

DOI10.1016/0362-546X(90)90018-CzbMath0702.35134OpenAlexW2045963057MaRDI QIDQ3480538

Jun Ning Zhao, Lambertus A. Peletier

Publication date: 1990

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(90)90018-c

zbMATH Keywords

Cauchy problemporous media equationsolvability criterionbehavior for t\(\searrow 0\)

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Flows in porous media; filtration; seepage (76S05) Fundamental solutions to PDEs (35A08) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (16)

Uniqueness of asymptotic profiles for an extinction problem ⋮ Large time behavior for the fast diffusion equation with critical absorption ⋮ Self-similar singular solutions of a \(p\)-Laplacian evolution equation with absorption ⋮ Source-type solutions of a singular conservation law with absorption ⋮ Global solutions of the fast diffusion equation with gradient absorption terms ⋮ Large time behaviour of solutions of the porous media equation with absorption: the fast diffusion case ⋮ Large time behavior of ODE type solutions to parabolic \(p\)-Laplacian type equations ⋮ Extinction of solutions to a diffusion problem with nonlinear sources and variable density ⋮ Nonlinear characterizations of stochastic completeness ⋮ Blow-up and global existence for the porous medium equation with reaction on a class of Cartan-Hadamard manifolds ⋮ Extinction for a fast diffusion equation with a nonlinear nonlocal source ⋮ Source-type solutions of degenerate quasilinear parabolic equations ⋮ Extinction and decay estimates of solutions for a class of porous medium equations ⋮ Extinction behaviour for fast diffusion equations with absorption ⋮ Singular solutions of parabolic $p$-Laplacian with absorption ⋮ The Cauchy problem for a singular conservation law with measures as initial conditions

Cites Work

• Nonlinear parabolic equations involving measures as initial conditions
• Classification of singular solutions of a nonlinear heat equation
• Source-type solutions of degenerate diffusion equations with absorption
• A very singular solution of the heat equation with absorption
• A very singular solution of the porous media equation with absorption
• Continuity of solutions of a singular parabolic equation

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