Controllability for a 2 × 2 nonlinear degenerate parabolic system via one boundary control force

In this paper we study the local boundary controllability for a non linear system of two degenerate parabolic equations with a control acting on only one equation. We analyze boundary null controllability properties for the linear system via the moment method by Fattorini and Russell, together with some results on biorthogonal families. Moreover, we provide an estimate on the null-control cost. This estimate let us prove a local exact boundary controllability result to zero of the nonlinear system following the iterative method from Lebeau and Robbiano as in [17,25].