scholarly journals Blow-up results for vector-valued nonlinear heat equations with no gradient structure

1998 ◽  
Vol 15 (5) ◽  
pp. 581-622 ◽  
Author(s):  
Hatem Zaag
Keyword(s):  
Blow Up ◽  
Heat Equations ◽  
Gradient Structure ◽  
Nonlinear Heat Equations ◽  
Vector Valued

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

On uniqueness for ODEs Arising in Blow-up Asymptotics for Nonlinear Heat Equations

2002 ◽  
Vol 2 (3) ◽  
Author(s):  
Manuela Chaves ◽  
Victor A. Galaktionov
Keyword(s):  
Blow Up ◽  
Reaction Diffusion ◽  
Similarity Solutions ◽  
Heat Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Singular Behaviour ◽  
Nonlinear Heat Equations ◽  
Self Similar ◽  
Similar Solutions ◽  
Diffusion Absorption

AbstractWe study uniqueness for nonlinear ordinary differential equations arising in constructing blow-up and extinction self-similar solutions of various reaction-diffusion- absorption equations. Such particular similarity solutions describe the asymptotic singular behaviour of wide classes of general solutions of nonlinear heat equations. We prove that under some monotonicity assumptions, such similarity profiles are unique.

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