Dead-core rates for the porous medium
equation with a strong absorption
Xinfu Chen - Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States (email)
Abstract: 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-similar dead-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.
Keywords: Dead-core rate, porous medium equation, strong absorption.
Received: March 2011; Revised: August 2011; Available Online: May 2012.
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