Construction of a blow-up solution for a perturbed nonlinear heat equation with a gradient and a non-local term
Analysis of PDEs
2020-07-03 v3
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. We prove the existence of a blow-up solution, and give its blow-up profile. Our proof relies on the following method: we linearize the equation (in similarity variables) around the expected profile, then, we control the nonpositive directions of the spectrum thanks to the decreasing properties of the kernel. Finally, we use a topological argument to control the positive directions of the spectrum.
Keywords
Cite
@article{arxiv.1911.06392,
title = {Construction of a blow-up solution for a perturbed nonlinear heat equation with a gradient and a non-local term},
author = {Bouthaina Abdelhedi and Hatem Zaag},
journal= {arXiv preprint arXiv:1911.06392},
year = {2020}
}