Null controllability of some nonlinear degenerate 1D parabolic equations

The main goal of the present paper is twofold: (i) to establish the well-posedness of a class of nonlinear degenerate parabolic equations and (ii) to investigate the related null controllability and decay rate properties. In a previous step, we consider an appropriate regularized system, where a small parameter α is involved. More precisely, the usual nonlinear term b(x)uux is replaced by b(x)zux, where z=(Id.−α2A)−1u and A is a Poisson-Dirichlet operator. We investigate the behavior of the null controls and their associated states as α → 0.