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Convergence rate for a semilinear parabolic equation with a singular nonlinearity

✍ Scribed by Masaki Hoshino

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 943 KB
Volume: 71
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2009.01.059

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✦ Synopsis

We study the behavior of solutions of the Cauchy problem for a semilinear parabolic equation with a singular power nonlinearity. It is known for a supercritical heat equation that if two solutions are initially close enough near the spatial infinity, then these solutions approach each other. In fact, given a specific decay rate of initial data, a sharp estimate of the convergence rate can be obtained explicitly. The main purpose of this research is to show a similar result for a semilinear parabolic equation with a singular absorption term. We also obtain a universal lower bound of the convergence rate which implies the optimality of the result. Proofs are given by a comparison method that is based on matched asymptotic expansion.

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