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:
76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
76L05 | Shock waves and blast waves in fluid mechanics |
35Q35 | PDEs in connection with fluid mechanics |
35L65 | Hyperbolic conservation laws |