A Nonlinear Parabolic Problem in an Exterior Domain

Author: Herraiz L.A.

Source: Journal of Differential Equations, Volume 142, Number 2, January 1998 , pp. 371-412(42)

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Abstract:

We consider the problem: Here p>1, N>=2, 0 isa finite union of disjoint open sets, and u o(x) is a continuous,nonnegative, and bounded function such that (0.4)u o(x)=~A |x|-alpha as |x|-<[infinity], for some A>0 and alpha>0. In this paper we discussthe asymptotic behaviour of solutions to (0.1)-(0.4) interms of the various values of the parameters p, A, N, Omega, andalpha. A common pattern that emerges from our analysis isthe existence of an external zone where u(x, t)=~u o(x),and one or several internal regions, where the influence ofthe set Omega, as well as that of diffusion and absorption, is moststrongly felt. We present a complete classification of the stabilizationprofiles in terms of these parameters. Copyright 1998 AcademicPress.

Language: English

Document Type: Research article

Affiliations: Departamento de Matematica Aplicada, Facultad de Matematicas, Universidad Complutense, Madrid, 28040, Spain

Publication date: 1998-01-01