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Sbornik: Mathematics, 2013, Volume 204, Issue 1, Pages 1–42
DOI: https://doi.org/10.1070/SM2013v204n01ABEH004290 (Mi sm8126) 		 
This article is cited in 26 scientific papers (total in 26 papers)

Regular attractors and nonautonomous perturbations of them

M. I. Vishika, S. V. Zelikb, V. V. Chepyzhovac

a Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Moscow
b University of Surrey, Guildford, United Kingdom
c National Research University Higher School of Economics, Moscow
English version PDF (609 kB) Citations (26)
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DOI: https://doi.org/10.1070/SM2013v204n01ABEH004290
Abstract: We study regular global attractors of dissipative dynamical semigroups with discrete or continuous time and we investigate attractors for nonautonomous perturbations of such semigroups. The main theorem states that the regularity of global attractors is preserved under small nonautonomous perturbations. Moreover, nonautonomous regular global attractors remain exponential and robust. We apply these general results to model nonautonomous reaction-diffusion systems in a bounded domain of $\mathbb R^3$ with time-dependent external forces.
Bibliography: 22 titles.
Keywords: dynamical semigroups and processes, regular attractors, uniform attractors, pullback attractors.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00339
10-01-00293
Ministry of Education and Science of the Russian Federation 8502
Received: 02.04.2012
Russian version:
Matematicheskii Sbornik, 2013, Volume 204, Number 1, Pages 3–46
DOI: https://doi.org/10.4213/sm8126
Bibliographic databases:
Document Type: Article
UDC: 517.956.8
MSC: Primary 35B41, 37B55, 35B40; Secondary 37C70, 37C60, 35K57
Language: English
Original paper language: Russian
Citation: M. I. Vishik, S. V. Zelik, V. V. Chepyzhov, “Regular attractors and nonautonomous perturbations of them”, Mat. Sb., 204:1 (2013), 3–46; Sb. Math., 204:1 (2013), 1–42
Citation in format AMSBIB
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    • This publication is cited in the following 26 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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