Journal
QUARTERLY OF APPLIED MATHEMATICS
Volume 59, Issue 2, Pages 315-342Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/qam/1827367
Keywords
multidimensional zero-pressure gas dynamics; delta-shock; vacuum; Riemann problem; stability; viscosity vanishing
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In this paper we study zero-pressure gas dynamics, which is a nonstrict hyperbolic system of nonlinear conservation laws with delta-shock waves in solutions. By using the generalized Rankine-Hugoniot relations to solve the Riemann problem with two pieces of constant initial data, multidimensional planar delta-shock waves dependent upon a family of one parameter are obtained. Furthermore! we choose a unique entropy solution through the process of a viscosity vanishing, and obtain a stability for delta shocks in multidimensions.
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