Feedback stabilization with one simultaneous control for systems of parabolic equations

Abstract

In this work controlled systems of semilinear parabolic equations are considered. Only one control is acting in both equations and it is distributed in a subdomain. Local feedback stabilization is studied. The approach is based on approximate controllability for the linearized system and the use of an appropriate norm obtained from a Lyapunov equation. Applications to reaction-diffusion systems are discussed.2010 Mathematics Subject Classification. 35K40, 35K57, 93D15, 93B52, 93B18.