Exact Controllability With Well-posedness And Regularity Of Partial Differential Equations Control Systems

In this paper, we study the exact controllability of three wave equations in Rn coupled in parallel and the well-posedness and regularity of an hyperbolic partial dif-ferential equations on a bounded domain of Rn, with Neumann control and collocated observation.Moreover, we prove that the system is not only well-posed in the sense of D.Salamon but also regular in the sense of G.Weiss.It is also shown that the corre-sponding feedthrough operator is zero.So,in this paper,we proved the exact controllability of three wave equations in Rn coupled in parallel and the well-posedness and regularity of the system as follow The thesis is organized as follows.In chapter l,we simply describe a research summary the exact controllability well-posedness and regularity of linear infinite-dimensional systems,and list some pre-liminaries of controllabled,well-posed and regular system.In chapter 2,we prove an exact controllability of three wave equations in Rn coupled in parallel.In chapter 3, we prove the well-posedness and regularity of the system of an hyperbolic partial differential equations with Neumann control and collocated obser-vation.