Delta-shocks as limits of vanishing viscosity for multidimensional zero-pressure gas dynamics

Li, Jiequan; Yang, Hanchun

doi:10.1090/qam/1827367

Authors: Jiequan Li and Hanchun Yang
Journal: Quart. Appl. Math. 59 (2001), 315-342
MSC: Primary 76N99; Secondary 35B35, 35L65, 35M20, 35Q35
DOI: https://doi.org/10.1090/qam/1827367
MathSciNet review: MR1827367
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Abstract: 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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