Internal feedback stabilization for parabolic systems coupled in zero or first order terms

Abstract

<p style='text-indent:20px;'>We consider systems of <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula> parabolic equations coupled in zero or first order terms with <inline-formula><tex-math id="M2">\begin{document}$ m $\end{document}</tex-math></inline-formula> scalar controls acting through a control matrix <inline-formula><tex-math id="M3">\begin{document}$ B $\end{document}</tex-math></inline-formula>. We are interested in stabilization with a control in feedback form. Our approach relies on the approximate controllability of the linearized system, which in turn is related to unique continuation property for the adjoint system. For the unique continuation we establish algebraic Kalman type conditions.