Geodesic
Criteria for the boundness of the solutions of the Cauchy problem for a~sistem of hyperbolic difference equations
Izvestiya. Mathematics , Tome 5 (1971) no. 3, pp. 711-718

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In the present article the difference analog of the Cauchy problem for a system of hyperbolic equations of second order is discussed. Conditions for the boundedness (for arbitrary bounded right-hand sides) of the solution of this problem are established for the case where the coefficients are constants or have weak variation at infinity. 
@article{IM2_1971_5_3_a11,
     author = {R. K. Romanovskii and A. M. Biberman},
     title = {Criteria for the boundness of the solutions of the {Cauchy} problem for a~sistem of hyperbolic difference equations},
     journal = {Izvestiya. Mathematics },
     pages = {711--718},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a11/}
}
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R. K. Romanovskii; A. M. Biberman. Criteria for the boundness of the solutions of the Cauchy problem for a~sistem of hyperbolic difference equations. Izvestiya. Mathematics , Tome 5 (1971) no. 3, pp. 711-718. http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a11/