| This dissertation is addressed to a study of the controllability for some coupled quasi-linear parabolic systems by one control force. We prove the local null controllability and the local approximate controllability for the coupled systems, respectively. In order to solve the quasilinear problems, we study the controllability of the linearized system in the framework of classical solutions. The key is to find a suitable control function in a Holder space such that the linearized system is null controllable by one control. Then, we apply Kakutani’s fixed point theorem to prove the local null controllability of the coupled quasilinear parabol-ic system. As a consequence, by the local well-posedness of coupled quasilinear parabolic systems, we prove the local approximate controllability for the associated controlled system. |
