Dynamics of second order in time evolution equations with state-dependent delay

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F15%3A00444708" target="_blank" >RIV/67985556:_____/15:00444708 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.na.2015.04.013" target="_blank" >http://dx.doi.org/10.1016/j.na.2015.04.013</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.na.2015.04.013" target="_blank" >10.1016/j.na.2015.04.013</a>

Result language
angličtina
Original language name
Dynamics of second order in time evolution equations with state-dependent delay
Original language description
We deal with a class of second order in time nonlinear evolution equations with state-dependent delay. This class covers several important PDE models arising in the theory of nonlinear plates. We first prove well-posedness in a certain space of functionswhich are C1 in time. In contrast with the first order models with discrete state-dependent delay this result does not require any compatibility conditions. The solutions constructed generate a dynamical system in a C1-type space over delay time interval. Our main result shows that this dynamical system possesses compact global and exponential attractors of finite fractal dimension. To obtain this result we adapt the recently developed method of quasi-stability estimates.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BD - Information theory
OECD FORD branch
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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

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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