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

2020/09/30 by Abdelhedi, Bouthaina, Zaag, Hatem
#35B20 #35B44 #35K55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.14641

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.

Related

• Refined blow-up asymptotics for a perturbed nonlinear heat equation with a gradient and a non-local term
• Sharp non-explicit blow-up profile for perturbed nonlinear heat equations with gradient terms
• Construction of a blow-up solution for a perturbed nonlinear heat\n equation with a gradient and a non-local term
• Existence of a Stable Blow-up profile for the nonlinear heat equation\n with a critical power nonlinear gradient term
• Sharp equivalent for the blowup profile to the gradient of a solution to the semilinear heat equation