In this paper we consider a class of quasi-linear hyperbolic systems, which allows the construction of a dissipative energy integrals. In the basis of the design and investigation the stability of difference schemes for the numerical solution of the initial boundary value problems for the above class of quasi-linear hyperbolic systems, we put the existence of a discrete analogue of the dissipative energy integrals.
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Aloev, Rakhmatillo and Khudayberganov, Mirzoali
"Using an a priori estimate for constructing difference schemes for quasi-linear hyperbolic systems,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 1:
1, Article 7.