Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F13%3A00381969" target="_blank" >RIV/67985556:_____/13:00381969 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.3934/dcds.2013.33.819" target="_blank" >http://dx.doi.org/10.3934/dcds.2013.33.819</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcds.2013.33.819" target="_blank" >10.3934/dcds.2013.33.819</a>
Alternative languages
Result language
angličtina
Original language name
Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space
Original language 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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BC - Theory and management systems
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP103%2F12%2F2431" target="_blank" >GAP103/12/2431: Systems described by partial differential equations with delays</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Continuous Dynamical Systems
ISSN
1078-0947
e-ISSN
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Volume of the periodical
33
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
819-835
UT code for WoS article
000309289900019
EID of the result in the Scopus database
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