Finite-dimensional feedback control of reaction-diffusion equations via inertial manifolds theory and applications to some evolutionary models

Time: 14:00 to  16:00 Ngày 07/04/2017

Venue/Location: C2-714

Speaker: Bùi Xuân Quang

Content:

The notion of inertial manifolds was introduced in 1985 by C. Foias, G.R. Sell and R. Temam. An inertial manifold is a (at least Lipschitz) smooth finite-dimensional manifold of the phase space which is positively invariant, attracts exponentially all orbits, and contains the global attractor. In this talk, using the inertial manifold theory for nonlinear evolution equations, I will construct a feedback controller for a class of control problems for one-dimensional nonlinear reaction-diffusion equations with the nonlinear term is $\varphi$-Lipschitz, for $\varphi$ belonging to an admissible space. Finally, I present two examples for evolutionary models motivated from nature to illustrate the feasibility of our results. This is a joint work with Nguyen Thieu Huy and Do Duc Thuan.