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Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay
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SYSNO ASEP 0444705 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay Author(s) Chueshov, I. (UA)
Rezunenko, Oleksandr (UTIA-B) RIDNumber of authors 2 Source Title Communications on Pure and Applied Analysis. - : AIMS Press - ISSN 1534-0392
Roč. 14, č. 5 (2015), s. 1685-1704Number of pages 20 s. Publication form Print - P Language eng - English Country US - United States Keywords Parabolic evolution equations ; state-dependent delay ; global attractor ; finite-dimension ; exponential attractor Subject RIV BC - Control Systems Theory R&D Projects GAP103/12/2431 GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000365023300005 EID SCOPUS 84930637032 DOI 10.3934/cpaa.2015.14.1685 Annotation We deal with a class of parabolic nonlinear evolution equations with state-dependent delay. This class covers several important PDE models arising in biology. We first prove well-posedness in a certain space of functions which are Lipschitz in time. This allows us to show that the model considered generates an evolution operator semigroup on a certain space of Lipschitz type functions over delay time interval. The operators are closed for all t greater than zero and continuous for t large enough. Our main result shows that the semigroup possesses compact global and exponential attractors of finite fractal dimension. Our argument is based on the recently developed method of quasi-stability estimates and involves some extension of the theory of global attractors for the case of closed evolutions. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2016
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