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2016 Blow-up results for a strongly perturbed semilinear heat equation: theoretical analysis and numerical method
Van Tien Nguyen, Hatem Zaag
Anal. PDE 9(1): 229-257 (2016). DOI: 10.2140/apde.2016.9.229

Abstract

We consider a blow-up solution for a strongly perturbed semilinear heat equation with Sobolev subcritical power nonlinearity. Working in the framework of similarity variables, we find a Lyapunov functional for the problem. Using this Lyapunov functional, we derive the blow-up rate and the blow-up limit of the solution. We also classify all asymptotic behaviors of the solution at the singularity and give precise blow-up profiles corresponding to these behaviors. Finally, we attain the blow-up profile numerically, thanks to a new mesh-refinement algorithm inspired by the rescaling method of Berger and Kohn. Note that our method is applicable to more general equations, in particular those with no scaling invariance.

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Van Tien Nguyen. Hatem Zaag. "Blow-up results for a strongly perturbed semilinear heat equation: theoretical analysis and numerical method." Anal. PDE 9 (1) 229 - 257, 2016. https://doi.org/10.2140/apde.2016.9.229

Information

Received: 25 November 2014; Revised: 20 August 2015; Accepted: 11 October 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 1334.35148
MathSciNet: MR3461306
Digital Object Identifier: 10.2140/apde.2016.9.229

Subjects:
Primary: 35K10
Secondary: 35K58

Rights: Copyright © 2016 Mathematical Sciences Publishers

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