| In the study of exact boundary controllability for the quasilinear vibrating string equation with boundary condition of the third type, we meet a kind of nonlocal mixed initial-boundary value problem of first order quasilinear hyperbolic system. In this paper, we establish the existence and uniqueness of semi-global Cl solution to the nonlocal mixed initial-boundary value problem, and obtain the exact boundary controllability for the corresponding problem. Especially, using a boundary control on one end, we get exact boundary controllability for the quasilinear vibrating equation with boundary condition of the third type on another end.The arrangement of the paper is as follows:In Chapter 1, we recall the definition, a brief history and present situation for the exact boundary controllability, and show the reduction to the nonlocal mixed initial-boundary value problem. The arrangement of the paper, the main results and methods as well as the sketches of proof are also included.Chapter 2 is devoted to the proof of the existence and uniqueness of semi-global Cl solution to the nonlocal mixed initial-boundary value problem for reducible quasilinear hyperbolic systems.Base on the results given in Chapter 2, and regarding the property of the quasilinear vibrating string equation and the boundary condition of the third kind, in Chapter 3 we prove that when a boundary condition of the 3rd type is given on one end, the exact boundary controllability of the string can be achieved through the boundary control in one of 3 kinds of boundary conditions of non-Dirichlet type on another end.In Chapter 4, we generalize the result on the semi-global Cl solution obtained in Chapter 2 to the general hyperbolic system, and then study the corresponding exactiiiboundary controllability with controls on both ends.In Appendix, the existence and uniqueness of global Cl solution to the Cauchy problem for a class of first order nonlocal quasilinear hyperbolic system are established.
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