Sharp non-explicit blow-up profile for perturbed nonlinear heat equations with gradient terms

Maissâ Boughrara

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arXiv · 2310.06620

Sharp non-explicit blow-up profile for perturbed nonlinear heat equations with gradient terms

Maissâ Boughrara

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Abstract

We consider a class of blow-up solutions for perturbed nonlinear heat equations involving gradient terms. We first prove the single point blow-up property for this equation and determine its final blow-up profile. We also give a sharper description of its blow-up behaviour, where we take as a profile some suitably chosen solution of the unperturbed semilinear heat equation. The proof relies on selfsimilar variables with involved arguments to control the gradient term.

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Maissâ Boughrara. 2023-10-10. Sharp non-explicit blow-up profile for perturbed nonlinear heat equations with gradient terms. https://arxiv.org/abs/2310.06620

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