Grow up and slow decay in the critical Sobolev case

DOI10.3934/nhm.2012.7.661zbMath1262.35032OpenAlexW1971148848MaRDI QIDQ1941637

John R. King, Marek Fila

Publication date: 21 March 2013

Published in: Networks and Heterogeneous Media (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/nhm.2012.7.661

zbMATH Keywords

Sobolev exponentmatched asymptotics

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Critical exponents in context of PDEs (35B33) Initial value problems for second-order parabolic equations (35K15) Semilinear parabolic equations (35K58)

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Decay rates for the 4D energy‐critical nonlinear heat equation ⋮ Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in \(\mathbb{R}^n\) ⋮ Finite time blow-up for the fractional critical heat equation in \(\mathbb{R}^n\) ⋮ Infinite time blow-up for critical heat equation with drift terms ⋮ Optimal Liouville theorems for superlinear parabolic problems ⋮ Infinite-time blow-up for the 3-dimensional energy-critical heat equation ⋮ Strongly anisotropic type II blow up at an isolated point

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