Stabilization of an interconnected system of Schrödinger and wave equations with boundary coupling

In this paper, we consider the Schrödinger equation coupled by interface with a wave and boundary damping. The dissipation is acting on through Neumann condition. We formulate system as an abstract evolution in appropriate Hilbert space use linear semigroup theory to show well-posedness of system. Then under some assumptions geometry spatial domain, prove exponential stability solution. proof result based frequency domain approach which consists verifying that imaginary axis included resolvent set analyzing behavior operator axis. analysis carried out combining contradiction argument multipliers technique. This extends Theorem 3.2 [13] multimensional domains.