SINGLE POINT BLOW-UP AND FINAL PROFILE FOR A PERTURBED NONLINEAR HEAT EQUATION WITH A GRADIENT AND A NON-LOCAL TERM

摘要

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, 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.