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Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit

Vishik, MI and Zelik, SV (2011) Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit arXiv.

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Abstract

We apply the dynamical approach to the study of the second order semi-linear elliptic boundary value problem in a cylindrical domain with a small parameter at the second derivative with respect to the "time" variable corresponding to the axis of the cylinder. We prove that, under natural assumptions on the nonlinear interaction function and the external forces, this problem possesses the uniform attractors and that these attractors tend to the attractor of the limit parabolic equation. Moreover, in case where the limit attractor is regular, we give the detailed description of the structure of these uniform attractors when the perturbation parameter is small enough, and estimate the symmetric distance between the perturbed and non-perturbed attractors.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Vishik, MIUNSPECIFIEDUNSPECIFIED
Zelik, SVUNSPECIFIEDUNSPECIFIED
Date : 9 October 2011
Related URLs :
Additional Information : Copyright 2014. Published by AIMS. All rights reserved. This article has been accepted for publication in Communications on Pure and Applied Analysis. This is an arXiv version of the paper, and is not the version of record.
Depositing User : Symplectic Elements
Date Deposited : 09 Jan 2015 09:24
Last Modified : 17 Jan 2015 14:46
URI: http://epubs.surrey.ac.uk/id/eprint/806845

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