Delta shock waves as limits of vanishing viscosity for 2-D steady pressureless isentropic flow
type: Item
instance of: scholarly article
title: Delta shock waves as limits of vanishing viscosity for 2-D steady pressureless isentropic flow
zbMATH Open document ID: 1216.35080
published in: Acta Applicandae Mathematicae
publication date: 2011-03-10T00:00:00Z
review text: The authors study the two-dimension steady pressureless isentropic flow described by the first-order system of equations (continuity equations and momentum conservation). The Riemann problem for this system is studied. This problem is solved by the characteristic method. Solutions are of two types: delta-shock solutions and vacuum solutions. The existence, uniqueness, and stability of the delta-shock solution is proved (under certain assumptions). The numerical examples illustrate the results.
reviewed by: Ilya A. Chernov
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35L67
zbMATH DE Number: 5864144
zbMATH Keywords: steady pressureless isentropic flow
zbMATH Keywords: delta shock
zbMATH Keywords: generalized Rankine-Hugoniot relation
zbMATH Keywords: entropy condition
zbMATH Keywords: Riemann problem
zbMATH Keywords: characteristic method
author: Hong Jun Cheng
author: Hanchun Yang
MaRDI profile type: Publication
full work available at URL: s10440-010-9602-6
OpenAlex ID: W1992674357
cites work: The Riemann problem for the transportation equations in gas dynamics
cites work: Q4265266
cites work: Delta-shocks as limits of vanishing viscosity for multidimensional zero-pressure gas dynamics
cites work: Two-dimensional Riemann problems for zero-pressure gas dynamics with three constant states
cites work: Well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge
cites work: Two-dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws. I: Four-\(J\) cases
cites work: Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws
cites work: Q3349303
cites work: Q3483714
cites work: \(\delta ^{\prime }\)-shock waves as a new type of solutions to systems of conservation laws
cites work: The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system
cites work: A high-order streamline Godunov scheme for steady supersonic flow computation.
cites work: A high-order streamline Godunov scheme for steady supersonic/hypersonic equilibrium flows
cites work: Non-oscillatory central differencing for hyperbolic conservation laws
DOI: 10.1007/S10440-010-9602-6
description: scientific article; zbMATH DE number 5864144