Null controllability of damped nonlinear wave equation

In this paper, we study the null controllability of nonlinear wave systems. Firstly, by combing Gerlerkin method and a fixed point theorem, we give the null controllability for semi-linear wave equation with nonlinear function dependents on velocities under the geometric control condition. Secondly, based on a new iterative method, we prove the null controllability for a class of quasi-linear wave system constructively. Finally, we give a control result for a class of fully nonlinear wave system as application.