The problems of blow-up for nonlinear heat equations. Complete blow-up and avalanche formation

zbMath1162.35392MaRDI QIDQ2504957

Juan Luis Vazquez

Publication date: 28 September 2006

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

zbMATH Keywords

Blow-upSemilinear heat equationsThermal avalanche

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Reaction-diffusion equations (35K57) Continuation and prolongation of solutions to PDEs (35B60)

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Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. I. ⋮ Blow-up versus global existence of solutions for reaction-diffusion equations on classes of Riemannian manifolds ⋮ Blow-up and global existence for the porous medium equation with reaction on a class of Cartan-Hadamard manifolds ⋮ Unnamed Item ⋮ Critical nonlinearities in partial differential equations ⋮ Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. II. ⋮ Smoothing effects and infinite time blowup for reaction-diffusion equations: an approach via Sobolev and Poincaré inequalities ⋮ Global existence of solutions and smoothing effects for classes of reaction-diffusion equations on manifolds ⋮ Nontrivial solutions for a nonlinear discrete elliptic equation with periodic boundary conditions ⋮ Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions ⋮ Blow-up and global existence for solutions to the porous medium equation with reaction and slowly decaying density

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