Null controllability of a semilinear degenerate parabolic equation with a gradient term

This paper concerns the null controllability of a semilinear control system governed by degenerate parabolic equation with a gradient term, where the nonlinearity of the problem is involved with the first derivative. We first establish the well-posedness and prove the approximate null controllability of the linearized system, then we can get the approximate null controllability of the semilinear control system by a fixed point argument. Finally, the semilinear control system with a gradient term is shown to be null controllable.