Transmission Problem Of Schr(?)dinger And Wave Equation With Viscous Damping

In this paper,we consider the transmission problem of a Schrodinger equation with a viscous damped wave equation which acts as a dynamic feedback controller of the Schrodinger equation.First,we show that the energy of the system is not increasing in time t,and give the system operator in the energy space.Next,by using the embeding theorem and the Lumer-Philips theorem,we prove the system operator generates a C0-semigroup of contractions,which guarantees the well-posedness of the system.Moreover,we use spectral analysis to show the eigenvalues of the system all locate in the left hand side of the complex plane and the imaginary axis is not an asymptote of the eigenvalues.Finally,we prove that the system is asymptotically stable.