Null controllability of coupled systems of degenerate parabolic integro-differential equations
Texas State University, Department of Mathematics
This article concerns the null controllability of a coupled system of two degenerate parabolic integro-differential equations with one locally distributed control force. Since the memory terms do not allow applying the standards Carleman estimates directly, we start by proving a null controllability result for an associated nonhomogeneous degenerate coupled system employing new Carleman estimates with appropriate weight functions. As a consequence, we deduce the null controllability result for the initial memory system by using the Kakutani's fixed point Theorem.
Carleman estimates, Parabolic systems involving memory terms, Observability inequality, Null controllability
Allal, B., Fragnelli, G., & Salhi, J. (2023). Null controllability of coupled systems of degenerate parabolic integro-differential equations. <i>Electronic Journal of Differential Equations, 2023</i>(18), pp. 1-22.