On Fast-Diffusion Equations with Infinite Equilibrium Entropy and Finite Equilibrium Mass

DOI10.1081/PDE-120019384zbMath1024.35040MaRDI QIDQ4805325

Claudia Lederman, Peter Alexander Markowich

Publication date: 12 May 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

large-time asymptoticsexponential convergenceconvection-diffusion equationsentropy-entropy dissipation approachgenealized Sobolev inequalitiesuniformly convex confinement potential

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Initial value problems for second-order parabolic equations (35K15)

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Cites Work

• On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds.
• ON CONVEX SOBOLEV INEQUALITIES AND THE RATE OF CONVERGENCE TO EQUILIBRIUM FOR FOKKER-PLANCK TYPE EQUATIONS
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• A Nonlinear heat equation with singular diffusivity
• Sur l'inégalité logarithmique de Sobolev
• Asymptotic L^1-decay of solutions of the porous medium equation to self-similarity
• A limit case in nonlinear diffusion
• Entropy dissipation methods for degenerate parabolic problems and generalized Sobolev inequalities

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