Controllability of degenerate parabolic equation with memory

In this paper, we analyze the null controllability property for a degenerate parabolic equation involving memory terms with a locally distributed control. We first derive a null controllability result for a nonhomogeneous degenerate heat equation via new Carleman estimates with weighted time functions that do not blow up at t= 0. Then this result is successfully used with a classical fixed point to obtain null controllability for the initial memory system.