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arXiv · 1404.4018

On the blow-up results for a class of strongly perturbed semilinear heat equations

Van Tien Nguyen
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Abstract

We consider in this work some class of strongly perturbed for the semilinear heat equation with Sobolev sub-critical power nonlinearity. We first derive a Lyapunov functional in similarity variables and then use it to derive the blow-up rate. We also classify all possible asymptotic behaviors of the solution when it approaches to singularity. Finally, we describe precisely the blow-up profiles corresponding to these behaviors.

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Van Tien Nguyen. 2014-04-15. On the blow-up results for a class of strongly perturbed semilinear heat equations. https://doi.org/10.3934/dcds.2015.35.3585

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