# American Institute of Mathematical Sciences

October  2013, 18(8): 2203-2210. doi: 10.3934/dcdsb.2013.18.2203

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

 1 Department of Applied Mathematics, National Chung Hsing University, 250, Kuo Kuang Road, Taichung 402, Taiwan 2 School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China

Received  September 2011 Revised  September 2012 Published  July 2013

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.
Citation: Chin-Chin Wu, Zhengce Zhang. Dead-core rates for the heat equation with a spatially dependent strong absorption. Discrete & Continuous Dynamical Systems - B, 2013, 18 (8) : 2203-2210. doi: 10.3934/dcdsb.2013.18.2203
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