Analysis and Applied Mathematics Seminar
Xiang Wan
Loyola University Chicago
Unique Continuation Properties of Static Eigen-Problems with Application to Uniform Stabilization of Dynamic Boussinesq Systems by Feedback Controllers
Abstract: In dealing with uniform stabilization of parabolic problems near an unstable equilibrium solution, the first critical step of what has become a standard strategy is to ascertain, if possible, Kalman's controllability condition of the projected finite dimensional unstable component. It was discovered about 15 years ago that this property is equivalent to establishing Unique Continuation Properties (UCPs) for the adjoint suitably over-determined eigen-problem.
In this talk, with focus on 2D-3D-Boussinesq systems (coupling the N-S with a diffusion equation), several UCPs of the adjoint systems are established to achieve the desired controllability results. These include the required UCPs for the localized interior as well as the localized boundary-based uniform stabilization of an unstable Boussinesq-system. We will also go through the idea of the proof, which follows the pointwise Carleman-type estimates approach.
Monday October 31, 2022 at 4:00 PM in 1227 SEO