| This thesis is mainly devoted to the study on the exact boundary controllability and observability for second-order quasilinear hyperbolic systems. By the result on the local exact boundary controllability and an extension method, the global exact boundary controllability for1-D quasilinear wave equations is obtained. Based on the theory of semi-global C2solutions to the mixed initial-boundary value problem for1-D quasilinear wave equations, by means of a direct constructive method, the author establishes the local and the global exact boundary controllability of nodal profile for1-D quasilinear wave equations. Then this result is generalized to the local exact boundary controllability of nodal profile for1-D quasilinear wave equations in a planar tree-like network of strings with general topology. At the end, the author introduces the concept of a kind of second-order quasilinear hyperbolic systems and realizes the local exact boundary controllability and observability for this system with general nonlinear boundary conditions.The arrangement of the thesis is as follows:First of all, in Chapter1, the author gives a brief introduction to the background and the present situation on the study of the exact controllability and observability.In Chapter2, by means of the known theory on the local exact boundary control-lability for1-D quasilinear wave equations, the global exact boundary controllability for them is obtained by an extension method. Similar result is also given for a general.kind of1-D quasilinear hyperbolic equations.Based on the theory of semi-global C2solutions to1-D quasilinear wave equations, the author adopts a direct constructive method and establishes the local exact boundary controllability of nodal profile for1-D quasilinear wave equations, and also obtains the corresponding global exact boundary controllability of nodal profile by means of the result given in Chapter2.In Chapter4, the author generalizes the result in Chapter3to the exact boundary controllability of nodal profile for1-D quasilinear wave equations in a planar tree-like network of strings with general topology.In Chapter5, the author proposes a kind of second-order quasilinear hyperbolic systems with nonlinear boundary conditions, the existence and uniqueness of the semi-global C2solution to them is considered under various cases, and the local exact boundary controllability for these second-order quasilinear hyperbolic systems is obtained by a direct constructive method.At last, in Chapter6, the author continues to discuss the second-order quasilinear hy-perbolic systems introduced in Chapter5, based on the theory of semi-global C2solution, the author obtains the local exact boundary observability for these second-order quasilin-ear hyperbolic systems. Moveover, some implicit dualities between the exact boundary controllability and the exact boundary observability are shown. |
