Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F15%3A00444705" target="_blank" >RIV/67985556:_____/15:00444705 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.3934/cpaa.2015.14.1685" target="_blank" >http://dx.doi.org/10.3934/cpaa.2015.14.1685</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/cpaa.2015.14.1685" target="_blank" >10.3934/cpaa.2015.14.1685</a>
Alternative languages
Result language
angličtina
Original language name
Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay
Original language description
We deal with a class of parabolic nonlinear evolution equations with state-dependent delay. This class covers several important PDE models arising in biology. We first prove well-posedness in a certain space of functions which are Lipschitz in time. Thisallows us to show that the model considered generates an evolution operator semigroup on a certain space of Lipschitz type functions over delay time interval. The operators are closed for all t greater than zero and continuous for t large enough. Our main result shows that the semigroup possesses compact global and exponential attractors of finite fractal dimension. Our argument is based on the recently developed method of quasi-stability estimates and involves some extension of the theory of global attractors for the case of closed evolutions.
Czech name
—
Czech description
—
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
—
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
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Communications on Pure and Applied Analysis
ISSN
1534-0392
e-ISSN
—
Volume of the periodical
14
Issue of the periodical within the volume
5
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
1685-1704
UT code for WoS article
000365023300005
EID of the result in the Scopus database
2-s2.0-84930637032