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

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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. 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. (en)
Title	Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space (en)
skos:prefLabel	Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space (en)
skos:notation	RIV/67985556:_____/13:00381969!RIV13-AV0-67985556
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP103/12/2431)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Zagalak, Petr
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	91986
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/13:00381969
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Partial differential equations with delays; well-posedness; metric space (en)
http://linked.open.../riv/klicoveSlovo	metric space Partial differential equations with delays well-posedness
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[1D30FFE3D34A]
http://linked.open...i/riv/nazevZdroje	Discrete and Continuous Dynamical Systems
http://linked.open...in/vavai/riv/obor	BC
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Systems described by partial differential equations with delays
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	33
http://linked.open...iv/tvurceVysledku	Zagalak, Petr Rezunenko, O. V.
http://linked.open...ain/vavai/riv/wos	000309289900019
issn	1078-0947
number of pages	21 (xsd:int)
http://bibframe.org/vocab/doi	10.3934/dcds.2013.33.819

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