Carleman Estimates and Null Controllability for Nonlinear Degenerate Parabolic Equations with Singular Lower Order Terms

Abstract

Abstract. This paper concerns the null controllability of a class of control systems governed by nonlinear degenerate parabolic equations with singular lower order terms. The equations are degenerate on a portion of the lateral boundary and their lower order terms are singular. We establish the Carleman estimates and the observability inequalities for linear equations by means of suitable weighted functions and a series of elaborate computations. Then the nonlinear control systems are shown to be null controllable.