Null controllability of nonlinear control systems governed by coupled degenerate parabolic equations

Abstract

This article concerns the null controllability of a nonlinear control system governed by coupled degenerate parabolic equations. We first establish the Carleman estimate and the observability inequality for solutions to the conjugate problem. Then we can prove the observability inequality and the null controllability of the linear control system. Finally, the nonlinear control system is shown to be null controllable by a fixed point argument and compact estimates.