17-23 Gianni Arioli, Hans Koch

Spectral stability for the wave equation with periodic forcing (508K, pdf) Mar 3, 17

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Abstract. We consider the spectral stability problem for Floquet-type systems such as the wave equation $v_{ au au}=\gamma^2 v_{xx}-\psi v$ with periodic forcing $\psi$. 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.

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