Dead-core rates for the porous medium equation with a strong absorption

We study the dead-core rate for the solution of the porous medium equation with a strong absorption.It is known that solutions with certain class of initial data develop a dead-core in finite time.We prove that, unlike the cases of semilinear heat equation and fast diffusion equation, there are solutions with the self-similardead-core rate. This result is based on the construction of a Lyapunov functional, some a priori estimates,and a delicate analysis of the associated re-scaled ordinary differential equation.