Interaction of three and four rarefaction waves of the pressure-gradient system

We study the two-dimensional pressure-gradient system, a subsystem of the two-dimensional compressible Euler system. We consider the problem of interaction of four rarefaction waves which is one case of two-dimensional Riemann problems. It is known that, when two planar waves interact, there exists a smooth solution in the interaction region. In this paper, we establish the existence of a smooth Solution in the hyperbolic domain of determinacy, in which we encounter the interaction or simple and planar waves and shock prevention in simple waves. (C) 2008 Elsevier Inc. All rights reserved.