. "Partial differential equations with delays; well-posedness; metric space"@en . "Zagalak, Petr" . . . . . "Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space"@en . "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\u201365]. 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\u2019s blowflies equation, all with state-dependent delays." . . . "I, P(GAP103/12/2431)" . "Discrete and Continuous Dynamical Systems" . "21"^^ . . . "2" . "RIV/67985556:_____/13:00381969!RIV13-AV0-67985556" . . . "Rezunenko, O. V." . "1078-0947" . "[1D30FFE3D34A]" . "RIV/67985556:_____/13:00381969" . "2"^^ . . "10.3934/dcds.2013.33.819" . "Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space" . "1"^^ . "33" . . . "Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space"@en . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . "Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space" . . . "000309289900019" . "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\u201365]. 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\u2019s blowflies equation, all with state-dependent delays."@en . "91986" .