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

2021/12/06 by Bouthaina Abdelhedi, Abdelhedi, Bouthaina, Hatem Zaag +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.2112.03039

openalex publication_date 2021/12/06 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28

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 ∇ 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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