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

0444708 - ÚTIA 2016 RIV GB eng J - Článek v odborném periodiku
Chueshov, I. - Rezunenko, Oleksandr
Dynamics of second order in time evolution equations with state-dependent delay.
Nonlinear Analysis: Theory, Methods & Applications. 123-124, č. 1 (2015), s. 126-149. ISSN 0362-546X. E-ISSN 1873-5215
Grant CEP: GA ČR GAP103/12/2431
Institucionální podpora: RVO:67985556
Klíčová slova: Second order evolution equations * State dependent delay * Nonlinear plate * Finite-dimensional attractor
Kód oboru RIV: BD - Teorie informace
Impakt faktor: 1.125, rok: 2015
http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444708.pdf

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 functions which 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.
Trvalý link: http://hdl.handle.net/11104/0247319