Stable shock waves in two-layer "shallow water"

A criterion is proposed for the correctness of a complete system of conversation laws which assumes the maximum compatibility between the domain of convexity of a closing conservation law and the domain of hyperbolicity of the differential mode I. A correct complete system of conservation laws is chosen on the basis of this criterion fur a model of two-layer "shallow water" with a free upper boundary in which the laws of conservation of mass in the layers, of total momentum and discontinuity in the velocity at the interface uf the lavers are the basic conservation laws and the law of conservation of the total energy is the closing conservation law. An analysis of the stable shock (intermittent) waves permitted by this system is presented. (C) 2001 Elsevier Science Ltd. Ail rights reserved.