In this paper the semilinear wave equation with homogeneous Dirichlet boundary condition having a locally distributed controller is considered, and the rapid exact controllability of this system is obtained by changin...In this paper the semilinear wave equation with homogeneous Dirichlet boundary condition having a locally distributed controller is considered, and the rapid exact controllability of this system is obtained by changing the shape and/or the location of the controller under proper conditions. For this purpose, the author derives an (rapid) observability inequality for wave equations with linear time-variant potential by means of the energy estimate. The main difference of the method from the previous ones is that any unique continuation property of the corresponding linear time-variant wave equations is not needed.展开更多
文摘In this paper the semilinear wave equation with homogeneous Dirichlet boundary condition having a locally distributed controller is considered, and the rapid exact controllability of this system is obtained by changing the shape and/or the location of the controller under proper conditions. For this purpose, the author derives an (rapid) observability inequality for wave equations with linear time-variant potential by means of the energy estimate. The main difference of the method from the previous ones is that any unique continuation property of the corresponding linear time-variant wave equations is not needed.
