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arXiv · 2112.03039

Refined blow-up asymptotics for a perturbed nonlinear heat equation with a gradient and a non-local term

Bouthaina Abdelhedi·Hatem Zaag
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Abstract

We consider in this paper a perturbation of the standard semilinear heat equation by a term involving the space derivative and a non-local term. In some earlier works [1, 2], we constructed a solution $u$ for that equation such that $u$ and $\nabla u$ both blow up at the origin and only there. We also gave the final blow-up profile. In this paper, we refine our construction method in order to get a sharper estimate on the gradient at blow-up.

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Bouthaina Abdelhedi, Hatem Zaag. 2021-12-06. Refined blow-up asymptotics for a perturbed nonlinear heat equation with a gradient and a non-local term. https://arxiv.org/abs/2112.03039

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