Spectral stability for the wave equation with periodic forcing

We consider the spectral stability problem for Floquet-type systems such as the wave equation vττ=γ2vxx−ψv with periodic forcing ψ. Our approach is based on a comparison with finite-dimensional approximations. Specific results are obtained for a system where the forcing is due to a coupling between the wave equation and a time-period solution of a nonlinear beam equation. We prove (spectral) stability for some period and instability for another. The finite-dimensional approximations are controlled via computer-assisted estimates.