Optimal rates of convergence to the singular Barenblatt profile for the fast diffusion equation

DOI10.1017/S0308210515000554zbMath1349.35168OpenAlexW2328251879MaRDI QIDQ5741034

Michael Winkler, Marek Fila

Publication date: 20 July 2016

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210515000554

zbMATH Keywords

fast diffusionnonlinear Fokker-Planck equationBarenblatt profileasymptotic behavior near extinction

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Second-order parabolic equations (35K10) Singular parabolic equations (35K67) Quasilinear parabolic equations (35K59) Fokker-Planck equations (35Q84)

Related Items

Very slow stabilization for a nonlinear Fokker-Planck equation, Singular extinction profiles of solutions to some fast diffusion equations, Special asymptotics for a critical fast diffusion equation, Singular limits and properties of solutions of some degenerate elliptic and parabolic equations, Asymptotic behaviour of singular solution of the fast diffusion equation in the punctured Euclidean space, One-dimensional super-fast diffusion: persistence versus extinction revisited -- extinction at spatial infinity, Asymptotic large time behavior of singular solutions of the fast diffusion equation, Sharp rate of convergence to Barenblatt profiles for a critical fast diffusion equation

Cites Work

• A continuum of extinction rates for the fast diffusion equation
• Grow up rate of solutions for a supercritical semilinear diffusion equation
• Degenerate diffusions. Initial value problems and local regularity theory
• Special fast diffusion with slow asymptotics: Entropy method and flow on a Riemannian manifold
• Asymptotics of the fast diffusion equation via entropy estimates
• Rate of convergence to a singular steady state of a supercritical parabolic equation
• Positivity, local smoothing, and Harnack inequalities for very fast diffusion equations
• Rate of convergence to Barenblatt profiles for the fast diffusion equation
• Special asymptotics for a critical fast diffusion equation
• Optimal lower bound of the grow-up rate for a supercritical parabolic equation
• Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent
• Radial fast diffusion on the hyperbolic space
• Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities