Blow-up in Nonlinear Heat Equations from the Dynamical Systems Point of View

2002 ◽  
pp. 723-758 ◽  
Author(s):  
Marek Fila ◽  
Hiroshi Matano
Keyword(s):  
Dynamical Systems ◽  
Blow Up ◽  
Point Of View ◽  
Heat Equations ◽  
Nonlinear Heat Equations

scholarly journals Blow-up of solutions of nonlinear heat equations

1988 ◽  
Vol 129 (2) ◽  
pp. 409-419 ◽  
Author(s):  
Luis A. Caffarrelli ◽  
Avner Friedman
Keyword(s):  
Blow Up ◽  
Heat Equations ◽  
Nonlinear Heat Equations

scholarly journals Blow-Up Time for Nonlinear Heat Equations with Transcendental Nonlinearity

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Hee Chul Pak
Keyword(s):  
Upper Bound ◽  
Blow Up ◽  
Heat Equations ◽  
Nonlinear Heat Equations

A blow-up time for nonlinear heat equations with transcendental nonlinearity is investigated. An upper bound of the first blow-up time is presented. It is pointed out that the upper bound of the first blow-up time depends on the support of the initial datum.

Convergence of blow-up solutions of nonlinear heat equations in the supercritical case

1999 ◽  
Vol 129 (6) ◽  
pp. 1197-1227 ◽  
Author(s):  
J. Matos
Keyword(s):  
Parabolic Equation ◽  
Heat Equation ◽  
Convergence Theorem ◽  
Nonlinear Parabolic Equation ◽  
Blow Up ◽  
Heat Equations ◽  
Semilinear Heat Equation ◽  
Nonlinear Parabolic ◽  
Nonlinear Heat Equations ◽  
Self Similar

In this paper, we study the blow-up behaviour of the radially symmetric non-negative solutions u of the semilinear heat equation with supercritical power nonlinearity up (that is, (N – 2)p> N + 2). We prove the existence of non-trivial self-similar blow-up patterns of u around the blow-up point x = 0. This result follows from a convergence theorem for a nonlinear parabolic equation associated to the initial one after rescaling by similarity variables.

scholarly journals Initial blow-up rates and universal bounds for nonlinear heat equations

2004 ◽  
Vol 196 (2) ◽  
pp. 316-339 ◽  
Author(s):  
Pavol Quittner ◽  
Philippe Souplet ◽  
Michael Winkler
Keyword(s):  
Blow Up ◽  
Heat Equations ◽  
Nonlinear Heat Equations ◽  
Universal Bounds
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