Large time behaviour of solutions of the porous media equation with absorption: the fast diffusion case

DOI10.1016/0362-546X(91)90059-AzbMath0762.35054OpenAlexW2049759489MaRDI QIDQ4008881

Lambertus A. Peletier, Jun Ning Zhao

Publication date: 27 September 1992

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

Full work available at URL: https://doi.org/10.1016/0362-546x(91)90059-a

zbMATH Keywords

comparisonuniqueness theorems

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Degenerate parabolic equations (35K65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Initial value problems for second-order parabolic equations (35K15)

Related Items (23)

Uniqueness of asymptotic profiles for an extinction problem ⋮ Large time behavior for the fast diffusion equation with critical absorption ⋮ Global solutions of the fast diffusion equation with gradient absorption terms ⋮ Unnamed Item ⋮ Extinction of solutions to a diffusion problem with nonlinear sources and variable density ⋮ Nonlinear characterizations of stochastic completeness ⋮ Large time behaviour of solutions of a fast diffusion equation with source ⋮ Long-time asymptotics for a 1D nonlocal porous medium equation with absorption or convection ⋮ 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 ⋮ Universal self-similarity of porous media equation with absorption: the critical exponent case. ⋮ Complicated asymptotic behavior of solutions for the fourth-order parabolic equation with absorption ⋮ A comparison principle for the porous media equation with absorption ⋮ Extinction behaviour for fast diffusion equations with absorption ⋮ Self-similar singular solution of doubly singular parabolic equation with gradient absorption term ⋮ Singular solutions of parabolic $p$-Laplacian with absorption ⋮ The existence of ground states to a weakly coupled elliptic system. ⋮ A porous media equation with absorption. I: Long time behaviour ⋮ A porous media equation with absorption. II: Uniqueness of the very singular solution ⋮ Large time behavior of ODE type solutions to nonlinear diffusion equations ⋮ Singular reaction diffusion equations of porous medium type ⋮ Fast diffusion on noncompact manifolds: Well-posedness theory and connections with semilinear elliptic equations ⋮ Relation between solutions and initial values for double-nonlinear diffusion equation

Cites Work

• Unnamed Item
• Unnamed Item
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• Large time behaviour of solutions of the porous media equation with absorption
• Large time behavior of the solutions of a semilinear parabolic equation in \(\mathbb R^ n\)
• On the behaviour as t\(\to \infty\) of the solutions of the Cauchy problem for certain nonlinear parabolic equations
• Uniqueness of solutions of the initial-value problem for \(u_t- \Delta\varphi (u)=0\)
• Source-type solutions of the porous media equation with absorption: The fast diffusion case
• The Cauchy Problem for u t = Δu m When 0 < m < 1
• Singular Solutions of the Heat Equation with Absorption
• The Asymptotic Behavior of Gas in an n-Dimensional Porous Medium

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