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

Abstract

<p style='text-indent:20px;'>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 [<xref ref-type="bibr" rid="b1">1</xref>], 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.