Periodic solutions for acousto-elastic scattering problems by controlling the time-dependent equations

The use of controllability methods for solving time-harmonic acousto-elastic wave equations is considered. In particular, the study concentrates on the coupling between two time-harmonic linear wave equations: the scalar valued Helmholtz equation concerning the propagation of acoustic waves and the vector valued Navier equation modeling the propagation of waves in an elastic medium. These fundamental equations occur in a number of physical applications such as acoustics, medicine, and geophysics. In this work, we concentrate on scattering problems but the same method can be used for other types of problems as well