English

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

Analysis of PDEs 2020-10-01 v1

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.

Keywords

Cite

@article{arxiv.2009.14641,
  title  = {Single point blow-up and final profile for a perturbed nonlinear heat equation with a gradient and a non-local term},
  author = {Bouthaina Abdelhedi and Hatem Zaag},
  journal= {arXiv preprint arXiv:2009.14641},
  year   = {2020}
}