On uniform attractors of explicit approximations
type: Item
instance of: scholarly article
title: On uniform attractors of explicit approximations
zbMATH Open document ID: 1236.65155
DOI: 10.1134/S0012266111040112
author: V. M. Ipatova
published in: Differential Equations
publication date: 2011-11-24T00:00:00Z
review text: The authors prove a theorem on the upper semicontinuous dependence on the parameter of the uniform attractors of a family of semiprocesses not necessarily having a common time semigroup. For a nonautonomous system of ordinary differential equations an explicit finite-difference scheme is suggested showing the existence of its attractor which lies in any neighborhood of the attractor of the original differential equation system for sufficiently small grid increments. Also for the vorticity equation on a rotating sphere with time-dependent bounded right-hand-side a finite-difference scheme is considered for which the existence of a uniform attractor is proved, approximating the true attractor of the original equation when the discretization parameter tends to zero.
Mathematics Subject Classification ID: 65P40
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 65L12
zbMATH DE Number: 5978700
zbMATH Keywords: dynamical systems
zbMATH Keywords: uniform attractors
zbMATH Keywords: attractors approximation
zbMATH Keywords: finite-difference scheme
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5978700