Some results on controllability of a nonlinear degenerate parabolic system by bilinear control ✩

In this paper, we discuss the controllability of a nonlinear degenerate parabolic system with bilinear control. Based on the shrinking property of the solutions, we prove that the system is not globally approximately controllable. Furthermore, we give an approximate null controllability result.We also prove that the system is not globally exactly null controllable by a comparison principle. © 2006 Elsevier Inc. All rights reserved