On the dead-core problem for the $p$-Laplace equation with a strong absorption

Abstract

We study an initial boundary value problem for the $p$-Laplace equation with a strong absorption. We are concerned with the dead-core behavior of the solution. First, some criteria for developing dead-core are given. Also, the temporal dead-core rate for certain initial data is determined. Then we prove uniqueness theorem for the backward self-similar solutions.