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Bibliografie

Journal Article

Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space

Rezunenko Oleksandr, Zagalak Petr

: Discrete and Continuous Dynamical Systems vol.33, 2 (2013), p. 819-835

: GAP103/12/2431, GA ČR

: Partial differential equations with delays, well-posedness, metric space

: 10.3934/dcds.2013.33.819

: http://library.utia.cas.cz/separaty/2012/AS/zagalak-0381969.pdf

(eng): 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.

: BC