Abstract:

In this paper, the author studies internal stabilization of steady-state
solutions to a class of semi-linear parabolic systems including three equations via finite-dimensional feedback controllers. The main idea is to use different internal controllers to stabilize different steady-state solutions. The controllers are provided by considering LQ problems associated with the linearized systems at steady-state solutions, and they are added to one, two or three
equations, depending on the considered steady-state solutions.

Key words: Stabilization, Parabolic system, Steady-state solution, Riccati equation, Feedback controller