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 $\Pi=\{(x,t)\colon0$ 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. 
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     author = {N. A. Lyul'ko},
     title = {On the instability of hyperbolic systems on the plane under small periodic perturbation},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {85--97},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2010_13_2_a8/}
}
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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/