On the pointwise behavior of the solutions of the porous medium equation as t approaches zero or infinity

DOI10.1016/0362-546X(85)90088-4zbMath0589.35064OpenAlexW1974213952MaRDI QIDQ3717513

Nicholas D. Alikakos

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0362-546x(85)90088-4

zbMATH Keywords

asymptotic behaviourporous medium equationsimilarity solutions

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25) Equations in function spaces; evolution equations (58D25)

Related Items (11)

An Upper Bound for the Waiting Time for Nonlinear Degenerate Parabolic Equations ⋮ Unnamed Item ⋮ Analytic semigroups, degenerate elliptic operators and applications to nonlinear Cauchy problems ⋮ Regularity of solutions and interfaces of a generalized porous medium equation in \(\mathbb{R}^ N\) ⋮ Upper bounds on waiting times for the thin-film equation: the case of weak slippage ⋮ The Waiting Time Phenomenon in Spatially Discretized Porous Medium and Thin Film Equations ⋮ An oscillating solution for the porous medium equation ⋮ On Lagrangian schemes for porous medium type generalized diffusion equations: a discrete energetic variational approach ⋮ Finite Speed of Propagation and Waiting Times for the Stochastic Porous Medium Equation: A Unifying Approach ⋮ On the uniformization of the solutions of the porous medium equation in \(R^ N\) ⋮ Finite Speed of Propagation and Waiting Time Phenomena for Degenerate Parabolic Equations with Linear Growth Lagrangian

Cites Work

• Unnamed Item
• Nonlinear parabolic equations involving measures as initial conditions
• On the uniformization of the solutions of the porous medium equation in \(R^ N\)
• Asymptotic behaviour of solutions of a nonlinear diffusion equation
• On a class of similarity solutions of the porous media equation. II
• Non-negative solutions of theo porous medium eqation
• A Fatou Theorem for Solutions of the Porous Medium Equation
• Decay of solutions of a degenerate nonlinear diffusion equation
• The Porous Medium Equation in One Dimension
• A class of similarity solutions of the nonlinear diffusion equation

This page was built for publication: On the pointwise behavior of the solutions of the porous medium equation as t approaches zero or infinity