Exact Controllability For Two Classes Of Partial Differential Equations

Partial differential equations arise in many fields, such as mathematics, physi-cal, and biological sciences, etc. In particular, the study of exact controllability for the partial differential equation has attracted considerable attention. The study of the exact controllability for partial differential equations has been a very active di-rection both in theory and practice. It is the core of the study of partial differential equations. It has important theoretical and practical significance. In this paper, we proved Schrodinger equation with inverse-square potential has internal exact control-lability and a class of weakly coupled wave equations with variable coefficients has exact boundary controllability.In the first chapter, we briefly introduce the background of the research, the trends of the research on partial differential equations and the content of the paper.In the second chapter, we study the problem of the internal exact controllability for the Schrodinger equation with inverse-square potential like λu/|x|~2. We prove the system has internal exact controllability in the space L2(Ω) with L2(Ω)-internal control.In the third chapter, we study the problem of the exact boundary controllability for a class of weakly coupled wave equations with variable coefficients. We prove the system has exact boundary controllability in the space L2(Ω)×H-1(Ω)with Lloc2(L2(Γ); (0, T))-boundary control.