Continuous dependence in thee large for some equations of gas dynamics

The main result of this paper is the construction of the Standard Riemann Semigroup for a class of 2 x 2 Conservation Laws without the requirement that the total variation of the initial data be small. For a class of equations of the form u(t) + [f(u)](x) = 0 with t greater than or equal to 0, x is an element of R, u is an element of R-2 (star) it is shown that there exists an L-1-Lipschitz continuous semigroup S defined on functions of bounded variation, such that the trajectories of S are weak entropy solutions to (star). This class includes the relativistic Euler equations, the equations of isentropic gas dynamics with gamma = 1, and all 2 x 2 Temple class systems.