Exact Boundary Controllability For Second Order Quasilinear Hyperbolic Equations

This thesis is divided into three parts.In the first part,we give the brief introduction to the exact controllability and the history of this study.In the second part,as a basis of further study,we prove the existence and uniqueness of semi-global C~2 solution to general second order quasilinear hyperbolic equations,based on the theory of the semi-global C~1 solution to the mixed initial-boundary value problem for first order quasilinear hyperbolic systems.In the third part,by means of the results obtained in part 2,we adopt a direct constructive method to obtain the local exact boundary controllability for general second order quasilinear hyperbolic equations with general nonlinear boundary conditions.