ON EXACT DEAD-CORE RATES FOR A SEMILINEAR HEAT EQUATION WITH STRONG ABSORPTION
Yukihiro Seki · Communications in Contemporary Mathematics · 2011
We study a semilinear heat equation with strong absorption ut = Δu - up with 0 < p < 1 in RN. A solution is known to develop dead-core in finite time for a wide class of initial data. We construct specific solutions with exact dead-core rates faster than the one given by the corresponding ODE. They are constructed formally by means of matched asymptotic expansion technique and rigorously by means of topological fixed-point arguments based on a priori estimates. To obtain the a priori estimates, we analyze a certain linearized problem in a new function space [Formula: see text].