scholarly journals Global solutions for a semilinear heat equation in the exterior domain of a compact set

2012 ◽  
Vol 32 (3) ◽  
pp. 847-865
Author(s):  
Kazuhiro Ishige ◽  
◽  
Michinori Ishiwata ◽  
Keyword(s):  
Heat Equation ◽  
Exterior Domain ◽  
Global Solutions ◽  
Compact Set ◽  
Semilinear Heat Equation

Asymptotically self-similar global solutions of a general semilinear heat equation

2001 ◽  
Vol 321 (1) ◽  
pp. 131-155 ◽  
Author(s):  
Seifeddine Snoussi ◽  
Slim Tayachi ◽  
Fred B. Weissler
Keyword(s):  
Heat Equation ◽  
Global Solutions ◽  
Semilinear Heat Equation ◽  
Self Similar

scholarly journals Global blow-up for a semilinear heat equation on a subspace

2015 ◽  
Vol 145 (5) ◽  
pp. 893-923 ◽  
Author(s):  
C. J. Budd ◽  
J. W. Dold ◽  
V. A. Galaktionov
Keyword(s):  
Heat Equation ◽  
Initial Function ◽  
Blow Up ◽  
Neumann Boundary ◽  
Compact Set ◽  
Sharp Estimates ◽  
Semilinear Heat Equation ◽  
Non Local ◽  
Image Position ◽  
Local Term

We study the asymptotic behaviour as t → T–, near a finite blow-up time T > 0, of decreasing-in-x solutions to the following semilinear heat equation with a non-local term:with Neumann boundary conditions and strictly decreasing initial function u0(x) with zero mass. We prove sharp estimates for u(x, t) as t → T–, revealing a non-uniform global blow-up:uniformly on any compact set [δ, 1], δ ∈ (0, 1).

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