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

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 works [1,2], we constructed a solution u for that equation such that u and ∇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.