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Delta-shocks as limits of vanishing viscosity for multidimensional zero-pressure gas dynamics. (English) Zbl 1019.76040
Summary: We study zero-pressure gas dynamics, which is a nonstrictly hyperbolic system of nonlinear conservation laws with delta-shock waves in solutions. By using generalized Rankine-Hugoniot relations to solve Riemann problem with two pieces of constant initial data, we obtain multidimensional planar delta-shock waves dependent upon a one-parametric family. Furthermore, we choose a unique entropy solution using the vanishing viscosity, and obtain a stability for delta-shocks.
MSC:
76N10Compressible fluids, general
76L05Shock waves; blast waves (fluid mechanics)
35Q35PDEs in connection with fluid mechanics
35L65Conservation laws