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arXiv · 2009.14641

Single point blow-up and final profile 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 work (Abdelhedi-Zaag JDE 2021), we constructed a blow-up solution for that equation, and showed that it blows up (at least) at the origin. We also derived the so called "intermediate blow-up profile". In this paper, we prove the single point blow-up property and determine the final blow-up profile.

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Bouthaina Abdelhedi, Hatem Zaag. 2020-09-30. Single point blow-up and final profile for a perturbed nonlinear heat equation with a gradient and a non-local term. https://arxiv.org/abs/2009.14641

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