| The present master thesis deals with the exact controllability for quasilinear hyperbolic systems with nonlinear boundary conditions.When the number of the positive eigenvalues is not equal to that of the negative ones,the author obtains the exact boundary controllability with less controls acting on two ends.The main constructive method is based on the theory on semiglobal C~1 solutions to the mixed initial-boundary value problem for general quasilinear hyperbolic systems.Besides,a sharp estimate on the control time is given.The arrangement of the thesis is as follows:First of all in Chapter 1,the author gives a brief introduction on the exact controllability.As a basis of further study,in Chapter 2,the author presents the existence and uniqueness of semiglobal C~1 solution to the mixed initial-boundary value problem for first order quasilinear hyperbolic systems with general nonlinear boundary conditions.The main result of this thesis,the exact boundary controllability with less controls acting on two ends for quailinear hyperbolic systems,will be presented in Chapter 3.In Chapter 4,the author extends the result obtained in Chapter 3 to the nonautonomous system.Chapter 5 is mainly devoted tp the case that the system has some zero eigenvalues.In Chapter 6,an application on high order hyperbolic equations is illustrated. |
