STRUCTURALLY STABLE RIEMANN SOLUTIONS

We study the structure of solutions of Riemann problems for systems of two conservation laws. Such a solution comprises a sequence of elemen tary waves, viz., rarefaction and shock waves of various types; shock waves are required to have viscous profiles. We construct a Riemann so lution by solving a system of equations characterizing its component w aves. A Riemann solution is ''structurally stable'' if the number and types of its component waves are preserved when the initial data and t he flux function are perturbed. Under the assumption that rarefaction waves and shock states lie in the stricly hyperbolic region, we charac terize Riemann solutions for which the definition equations have maxim al rank and we prove that such solutions are structurally stable. Stru cturally stable Riemann solutions cannot contain overcompressive shock waves, but they can contain transitional shock waves, including doubl y sonic transitional shock waves, including doubly sonic transitional shock waves that have not been observed before. (C) 1996 Academic Pres s, Inc.