| bibtype |
J -
Journal Article
|
| ARLID |
0444705 |
| utime |
20240103210150.7 |
| mtime |
20150617235959.9 |
| WOS |
000365023300005 |
| SCOPUS |
84930637032 |
| DOI |
10.3934/cpaa.2015.14.1685 |
| title
(primary) (eng) |
Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay |
| specification |
| page_count |
20 s. |
| media_type |
P |
|
| serial |
| ARLID |
cav_un_epca*0258111 |
| ISSN |
1534-0392 |
| title
|
Communications on Pure and Applied Analysis |
| volume_id |
14 |
| volume |
5 (2015) |
| page_num |
1685-1704 |
| publisher |
|
|
| keyword |
Parabolic evolution equations |
| keyword |
state-dependent delay |
| keyword |
global attractor |
| keyword |
finite-dimension |
| keyword |
exponential attractor |
| author
(primary) |
| ARLID |
cav_un_auth*0317550 |
| name1 |
Chueshov |
| name2 |
I. |
| country |
UA |
|
| author
|
| ARLID |
cav_un_auth*0282033 |
| name1 |
Rezunenko |
| name2 |
Oleksandr |
| full_dept (cz) |
Adaptivní systémy |
| full_dept |
Department of Adaptive Systems |
| department (cz) |
AS |
| department |
AS |
| institution |
UTIA-B |
| full_dept |
Department of Adaptive Systems |
| fullinstit |
Ústav teorie informace a automatizace AV ČR, v. v. i. |
|
| source |
|
| cas_special |
| project |
| project_id |
GAP103/12/2431 |
| agency |
GA ČR |
| ARLID |
cav_un_auth*0284932 |
|
| abstract
(eng) |
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. This allows 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. |
| reportyear |
2016 |
| RIV |
BC |
| num_of_auth |
2 |
| mrcbC52 |
4 A hod 4ah 20231122141012.7 |
| inst_support |
RVO:67985556 |
| permalink |
http://hdl.handle.net/11104/0247320 |
| mrcbC64 |
1 Department of Adaptive Systems UTIA-B 10101 MATHEMATICS |
| confidential |
S |
| mrcbT16-e |
MATHEMATICS|MATHEMATICSAPPLIED |
| mrcbT16-j |
0.7 |
| mrcbT16-s |
1.194 |
| mrcbT16-4 |
Q1 |
| mrcbT16-B |
54.742 |
| mrcbT16-C |
68.488 |
| mrcbT16-D |
Q2 |
| mrcbT16-E |
Q1 |
| arlyear |
2015 |
| mrcbTft |
\nSoubory v repozitáři: rezunenko-0444705.pdf |
| mrcbU14 |
84930637032 SCOPUS |
| mrcbU34 |
000365023300005 WOS |
| mrcbU63 |
cav_un_epca*0258111 Communications on Pure and Applied Analysis 1534-0392 1553-5258 Roč. 14 č. 5 2015 1685 1704 AIMS Press |
|