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A limiting viscosity approach to Riemann solutions containing delta-shock waves for nonstrictly hyperbolic conservation laws. (English) Zbl 0877.35076
The paper describes the analysis of a nonstrictly hyperbolic system of conservation laws which can be achieved from the momentum equations of the two-dimensional compressible Euler equations by introducing the assumptions of constant pressure in space and constant density in space and time. Thereby, a Riemann problem with constant left and right initial values is considered. In the first part, the author shows that the viscosity regularized problem generated by adding a small time dependent viscous perturbation into both equations has a smooth self-similar solution, if the above-mentioned initial values are considered. Furthermore, a proof is given that the limit solutions of the perturbed system generate solutions of the Riemann problem.
##### MSC:
 35L65 Conservation laws