学术报告

报告人：Igor Chueshov (Kharkov National University, Ukraine)

报告摘要：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 $S_t$ on a space of Lipschitz type functions over delay time interval. The operators $S_t$ are closed for all $t\ge 0$ and continuous for $t$ large enough. We show that the semigroup $S_t$ possesses compact global and exponential attractors of finite fractal dimension. Our argument relies 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. The talk is based on results which were obtained in collaboration with Alexander Rezounenko.

报告题目：Dynamics in parabolic PDE with state-dependent delay

报告时间：2015年11月11日（星期三） 上午11:00

报告地点：科技楼南楼702