Carleman Estimates and Null Controllability for a Class of Degenerate Parabolic Equations with Convection Terms

This paper concerns a class of control systems governed by semilinear degenerate parabolic equations with convection terms, which cannot be controlled by the diffusion terms. The Carleman estimates and the observability inequalities for the corresponding linear equations are established if the degeneracy is relatively weak. Subsequently, it is proved that the control systems are null controllable.