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For the difference scheme approximating the gas dynamics problem in Riemann invariants a priory estimates with respect 			to the initial data have been obtained. These estimates are proved without any assumptions about the solution of the 			differential problem using only limitations for the initial and boundary conditions. Estimates of stability in the general 			case have been obtained only for the finite instant of time. The uniqueness and convergence 			of the difference solution are also considered. The results of the numerical experiment confirming theoretical results are given.

Nonlinear Stability Of The Difference Schemes For Equations Of Isentropic Gas Dynamics