An Inverse Problem for the Forced Transverse Vibration of a Rectangular Membrane with Time Dependent Potential

Abstract

In this paper, an initial-boundary value problem for a two-dimensional waveequation which arises in the equation of motion for the forced transverse vibration of a rectangular membrane is considered. Giving an additional condition, a time-dependentcoefficient is determined and existence anduniqueness theorem for smalltimes is proved.Moreover, characterization of the conditional stability isgivenand numerical solution of the inverse probleminvestigatedby using finite difference method.