Internal feedback stabilization of nonstationary solutions to semilinear parabolic systems (Q328459)

The paper is devoted to systems of controlled parabolic equations, coupled in their zero- and first-order terms. The author analyses the case where the controller is distributed in a subdomain where the system is defined. The main result of the work consists in construction of a feedback stabilizing controller, by associating an appropriate, quadratic and optimal control problem with infinite horizon. The cost is a quadratic form associated with some operator, which satisfies a corresponding Riccati equation. The feedback is constructed using this operator and is showed to be stabilizing both in the linear and the nonlinear cases.