Observability Of One Dimensional Evolution Equation On Trapezoidal Domain

In this thesis,we mainly discuss the interior observability of one-dimensional wave equation with mixed boundary in trapezoidal domain and the boundary observability of Schrodinger equation with mixed boundary in trapezoidal domain.The thesis consists of three chapters.In Chapter 1,in this thesis,some problems about observability of one-dimensional wave equation are briefly introduced,and the main problems of this thesis are given.In Chapter 2,Consider the following system on trapezoidal region?={(x,t)?R2:0 ?x? s(t),t? t0}s(t)=lt,t?t0 where(g,f)?HR1[0,lt0]×L2[0,lt0],HR1[0,lt0]={g?H1[0,lt0]|g(lt0)=0} is any given initial value.With the help of generalized Fourier series and the Parseval equation in weighted L2-space,the observability inequalities of internal fixed point and internal moving point are derived respectively,and the simultaneous exact controllability of the corresponding coupled system is obtained.In Chapter 3,in this thesis,the observability of Schrodinger equation with Mixed boundary on a trapezoidal domain with l(t)=1+?t at one end is considered.Order l(t)=1+?t,? ?(0,2/?),0<t<1/?(2/??-1)we discuss the observability of the following systems:...