Exact Controllability For The One-Dimensional Degenerate Schr?dinger Equation

In this thesis,the exact controllability of one-dimensional degenerate Schrodinger equation under the action of boundary control or interior control are discussed.The multiplier method is used to establish the observability inequality of the dual system,and then prove the exact controllability of the control system by Hilbert Uniqueness Method.The thesis is arranged as follows.Chapter 1 is the introduction.We mainly introduce the background of the research problem and the research status at home and abroad.Chapter 2 gives a preliminary knowledge of what will be studied in this thesis.In Chapter 3,the exact boundary controllability of one-dimensional degenerate Schrodinger equation as follows is studied(?)Select a suitable multiplier and then use the multiplier techniques and Hilbert Uniqueness Method to find the appropriate control,thereby,the exact boundary controllability is obtained.Chapter 4 considers the exact interior controllability of the following one-dimensional degenerate Schrodinger equation(?)When the control acts on a subset of(0,1),we determine the appropriate control h by analyzing the relationship between the space L~2(0,1)and weighted Sobolev space H_k~1(0,1).Next,the exact interior controllability problem is considered through the interpolation and Hilbert Uniqueness Method.Chapter 5 gives some summaries about the problems studied in this thesis.