Construction of a blow-up solution for a perturbed nonlinear heat\n equation with a gradient and a non-local term

2019/11/14 by Bouthaina Abdelhedi, Abdelhedi, Bouthaina, Hatem Zaag +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1911.06392

openalex publication_date 2019/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider in this paper a perturbation of the standard semilinear heat\nequation by a term involving the space derivative and a non-local term. We\nprove the existence of a blow-up solution, and give its blow-up profile. Our\nproof relies on the following method: we linearize the equation (in similarity\nvariables) around the expected profile, then, we control the nonpositive\ndirections of the spectrum thanks to the decreasing properties of the kernel.\nFinally, we use a topological argument to control the positive directions of\nthe spectrum.\n

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