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Journal Article

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

Chueshov I., Rezunenko Oleksandr

: Nonlinear Analysis: Theory, Methods & Applications, 1 (2015), p. 126-149

: GAP103/12/2431, GA ČR

: Second order evolution equations, State dependent delay, Nonlinear plate, Finite-dimensional attractor

: 10.1016/j.na.2015.04.013

: http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444708.pdf

(eng): 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.

: BD

07.01.2019 - 08:39