0444705 20240103210150.720150617235959.9 000365023300005 84930637032 10.3934/cpaa.2015.14.1685 20 s. P cav_un_epca*02581111534-0392145 (2015)1685-1704AIMS Press Parabolic evolution equations state-dependent delay global attractor finite-dimension exponential attractor cav_un_auth*0317550 Chueshov I. UA cav_un_auth*0282033 Rezunenko Oleksandr Adaptivní systémy Department of Adaptive Systems AS AS UTIA-B Department of Adaptive Systems Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444705.pdf GAP103/12/2431 GA ČR cav_un_auth*0284932 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. 2016 BC 2 4 A hod 4ah 20231122141012.7 RVO:67985556 http://hdl.handle.net/11104/0247320 1 Department of Adaptive Systems UTIA-B 10101 MATHEMATICS S MATHEMATICS|MATHEMATICS.APPLIED 0.906 0.173 4.9 0.00672 0.7 998 1.194 Q1 0.848 133 Q1 54.742 68.5 Q2 Q1 77.724 2015 Soubory v repozitáři: rezunenko-0444705.pdf 84930637032 SCOPUS 000365023300005 WOS cav_un_epca*0258111 Communications on Pure and Applied Analysis 1534-0392 1553-5258 Roč. 14 č. 5 2015 1685 1704 AIMS Press