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

doi:10.3934/dcdss.2021032

Article Contents

2021, Volume 14, Issue 8: 2607-2623. Doi: 10.3934/dcdss.2021032

This issue Previous Article Preface Next Article Non-standard boundary conditions for the linearized Korteweg-de Vries equation

Single point blow-up and final profile for a perturbed nonlinear heat equation with a gradient and a non-local term

Bouthaina Abdelhedi^1, and
Hatem Zaag^2,

1.
Université de Sfax, Faculté des Sciences de Sfax, Département de Mathematiques, BP 1171, Sfax 3000, Tunisia
2.
Université Sorbonne Paris Nord, Institut Galilée, Laboratoire Analyse, Géométrie et Applications, CNRS UMR 7539, 99 avenue J.B. Clément, 93430 Villetaneuse, France

Dedicated to the memory of Ezzeddine Zahrouni

Received: September 2020

Revised: February 2021

Early access: March 2021

Published: August 2021

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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 [1], 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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Mathematics Subject Classification: 35B20, 35B44, 35K55.

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References

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