A Kind Of Controllability Problems About Semilinear Euler-Bernouli Equation

In this paper we consider a kind of controllability problems about semilinear plate equa-tion,which has profoundly physical background and has been paid much attention by many mathematicians and physical scientists for a long time. There have been some results in the search field including properties and some controllability about this system. Based on these results we study a kind of controllability problems and obtain some satisfying results.The paper is composed of the following three sections.In section l,we generally introduce the known correlative results about the problems of boundary controllability.And we refer to the key theorem we use in my paper.In section 2,we analyze exact controllability problem about semilinear plate equation with one-variable boundary. At first, we transform the eqations into the abstract equation,under the framework of abstract equations,combining the theorems in [l],we convert the controllability problems in original system.Finally using the method in [8],we study observability problems and obtain the desired results.In section 3 ,we analyze the exact controllability problem about semilinear plate equation with Neumann-boundary. The martingale is similar with one used in section 2. Obviously compared with the first problem the difficulty is much larger,and it is pretty necessary because this boundary condition is more spontaneous.