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.