0381969 20240103201350.920121029235959.9 000309289900019 10.3934/dcds.2013.33.819 21 s. cav_un_epca*02558981078-0947332 (2013)819-835AIMS Press Partial differential equations with delays well-posedness metric space 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. cav_un_auth*0101234 Zagalak Petr 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/2012/AS/zagalak-0381969.pdf GAP103/12/2431 GA ČR CZ cav_un_auth*0284932 Partial differential equations with discrete (concentrated) state-dependent delays are studied. The existence and uniqueness of solutions with initial data from a wider linear space is proven first and then a subset of the space of continuously differentiable (with respect to an appropriate norm) functions is used to construct a dynamical system. This subset is an analogue of the solution manifold proposed for ordinary equations in [H.-O. Walther, The solution manifold and C 1-smoothness for differential equations with state- dependent delay, J. Differential Equations, 195(1), (2003) 46–65]. The exis- tence of a compact global attractor is proven. As applications, we consider the well known Mackey-Glass-type equations with diffusion, the Lasota-Wazewska- Czyzewska model, and the delayed diffusive Nicholson’s blowflies equation, all with state-dependent delays. 2013 BC 4 A 4a 20231122135241.3 RVO:67985556 http://hdl.handle.net/11104/0212323 MATHEMATICS|MATHEMATICSAPPLIED 1.076 0.280 5.0 0.01767 1.059 2048 357 1.375 ScienceCitationIndex Q1 82.469 73.246 Q1 Q1 2013 Soubory v repozitáři: zagalak-0381969.pdf 000309289900019 WOS cav_un_epca*0255898 Discrete and Continuous Dynamical Systems 1078-0947 1553-5231 Roč. 33 č. 2 2013 819 835 AIMS Press