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2008 Finite time dead-core rate for the heat equation with a strong absorption
Jong-Shenq Guo, Chin-Chin Wu
Tohoku Math. J. (2) 60(1): 37-70 (2008). DOI: 10.2748/tmj/1206734406


We study the solution of the heat equation with a strong absorption. It is well-known that the solution develops a dead-core in finite time for a large class of initial data. It is also known that the exact dead-core rate is faster than the corresponding self-similar rate. By using the idea of matching, we formally derive the exact dead-core rates under a dynamical theory assumption. Moreover, we also construct some special solutions for the corresponding Cauchy problem satisfying this dynamical theory assumption. These solutions provide some examples with certain given polynomial rates.


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Jong-Shenq Guo. Chin-Chin Wu. "Finite time dead-core rate for the heat equation with a strong absorption." Tohoku Math. J. (2) 60 (1) 37 - 70, 2008.


Published: 2008
First available in Project Euclid: 28 March 2008

zbMATH: 1157.35059
MathSciNet: MR2419036
Digital Object Identifier: 10.2748/tmj/1206734406

Primary: 35K57
Secondary: 34B16, 35K55

Rights: Copyright © 2008 Tohoku University


Vol.60 • No. 1 • 2008
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