arXiv subjects

Bouthaina Abdelhedi

Publications and source records attributed to Bouthaina Abdelhedi.

3 recordsLinked to original sources

arXiv2021

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

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 $\nabla u$ 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.

math.AP↗

arXiv2020

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

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.

math.AP↗

arXiv2020

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

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.

math.AP↗