Null controllability for a class of degenerate parabolic equations with the gradient terms

Abstract

This paper concerns a class of control systems governed by degenerate parabolic equations with the gradient terms, which are independent of the diffusion terms. The Carleman estimates and the observability inequalities for the equations are established when the degeneracy is relatively weak. Subsequently, it is proved that the control systems are null controllable. Moreover, the result can be generalized to the semilinear equations by using the fixed point theorem.