Regional Gradient Stabilization of Semilinear Distributed Systems

This paper deals with regional stabilization of the gradient of semilinear distributed system evolving on a spatial domain Ω. It consists in studying the asymptotic behavior of gradient of such a system in a subregion ω of Ω. Then we characterize gradient stabilizing controls, and the one that stabilizes the gradient on ω and minimizes a given performance cost. The developed results are successfully illustrated by simulations.