Sharp estimates of the convergence rate for a semilinear parabolic equation with supercritical nonlinearity |
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Authors: | Masaki Hoshino Eiji Yanagida |
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Institution: | Mathematical Institute, Tohoku University, Sendai 980-8578, Japan |
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Abstract: | We study the behavior of solutions of the Cauchy problem for a semilinear parabolic equation with supercritical nonlinearity. It is known that if two solutions are initially close enough near the spatial infinity, then these solutions approach each other. In this paper, we give its sharp convergence rate for a class of initial data. We also derive a universal lower bound of the convergence rate which implies the optimality of the result. Proofs are given by a comparison method based on matched asymptotics expansion. |
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Keywords: | 35K15 35B35 35B40 |
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