Source: Tohoku Math. J. (2) Volume 60, Number 1
(2008), 37-70.
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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