The Cauchy problem for some models of one-dimensional gas dynamics (Q1385973)

I prove theorems of existence of generalized solutions (in the sense of the distribution theory) to some systems of conservation laws with two independent variables. I study here the so-called Glimm scheme in application to the systems of equations that are connected with one-dimensional gas dynamics. A theorem for the existence of the generalized solution to the system of \(N\) conservation laws with two independent variables was proved with the help of the Glimm scheme. However, it was assumed there that initial functions have small variation, i.e., are slightly different from constants. I assume only that initial data have bounded variation, and also assume that the statements of maximum principle type are valid.