Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Dead-core rates for the heat equation with a spatially dependent strong absorption

Pages: 2203 - 2210, Volume 18, Issue 8, October 2013      doi:10.3934/dcdsb.2013.18.2203

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Chin-Chin Wu - Department of Applied Mathematics, National Chung Hsing University, 250, Kuo Kuang Road, Taichung 402, Taiwan (email)
Zhengce Zhang - School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China (email)

Abstract: 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.

Keywords:  Dead-core, heat equation, strong absorption.
Mathematics Subject Classification:  Primary: 35K20, 35K55; Secondary: 35B40.

Received: September 2011;      Revised: September 2012;      Available Online: July 2013.