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Asymptotic Behaviour of Solutions to some Pseudoparabolic Equations

✍ Scribed by Grzegorz Karch

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 336 KB
Volume: 20
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(199702)20:3<271::aid-mma859>3.0.co;2-f

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✦ Synopsis

The aim of this paper is to investigate the behaviour as tP R of solutions to the Cauchy problem

, where '0 is a fixed constant, t*0, x31L. First, we prove that if u is the solution to the linearized equation, i.e. with • F(u),0, then u decays like a solution for the analogous problem to the heat equation. Moreover, the long-time behaviour of u is described by the heat kernel. Next, analogous results are established for the non-linear equation with some assumptions imposed on F, p, and the initial condition u .

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