Geodesic
On the instability of hyperbolic systems on the plane under small periodic perturbation
Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 2, pp. 85-97

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For a strictly hyperbolic linear first order system in the half-strip $\Pi=\{(x,t)\colon00\}$ 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.
Keywords: the mixed problem for a hyperbolic system on the plane, instability of solutions, averaging method. 
N. A. Lyul'ko. On the instability of hyperbolic systems on the plane under small periodic perturbation. Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 2, pp. 85-97. http://geodesic.mathdoc.fr/item/SJIM_2010_13_2_a8/
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