On the instability of hyperbolic systems on the plane under small periodic perturbation

For a strictly hyperbolic linear first order system in the half-strip $\Pi=\{(x,t)\colon0<x<1,\ t>0\}$ we consider the mixed problem generating a group of unitary operators. In the case of a periodic perturbation we propose a method for finding the frequencies for which the perturbed system develops parametric resonance. We illustrate the method with a system of two equations.