Gianni Arioli, Hans Koch
Spectral stability for the wave equation with periodic forcing
(508K, pdf)

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.