DEAD-CORE RATES FOR THE HEAT EQUATION WITH ASPATIALLY DEPENDENT STRONG ABSORPTION

摘要

This work is to study the dead-core behavior for a semilinear heat equation with a spatially dependent strong absorption term. We first give a criterion on the initial data such that the dead-core occurs. Then we prove the temporal dead-core rate is non-self-similar. This is based on the standard limiting process with the uniqueness of the self-similar solutions in a certain class.