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Bibliography

Journal Article

Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay

Chueshov I., Rezunenko Oleksandr

: Communications on Pure and Applied Analysis vol.14, 5 (2015), p. 1685-1704

: GAP103/12/2431, GA ČR

: Parabolic evolution equations, state-dependent delay, global attractor, finite-dimension, exponential attractor

: 10.3934/cpaa.2015.14.1685

: http://library.utia.cas.cz/separaty/2015/AS/rezunenko-0444705.pdf

(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.

: BC

2019-01-07 08:39