Null controllability of some nonlinear degenerate 1D parabolic equations

Abstract 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 ) uu x is replaced by b ( x ) zu x , where z = ( Id . − α 2 A ) − 1 u and A is a Poisson–Dirichlet operator. We investigate the behavior of the null controls and their associated states as  α  → 0.