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Tohoku Mathematical Journal
SECOND SERIES VOL. 60, NO. 1
|Tohoku Math. J.|
60 (2008), 37-70
FINITE TIME DEAD-CORE RATE FOR THE HEAT EQUATION WITH A STRONG ABSORPTION
Jong-Shenq Guo and Chin-Chin Wu
(Received October 10, 2006, revised May 1, 2007)
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.
2000 Mathematics Subject Classification.
Primary 35K57; Secondary 35K55, 34B16.
Key words and phrases.
dead-core, dead-core rate, heat equation, absorption.
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