Delta shock waves for a linearly degenerate hyperbolic system of conservation laws of Keyfitz-Kranzer type
type: Item
instance of: scholarly article
title: Delta shock waves for a linearly degenerate hyperbolic system of conservation laws of Keyfitz-Kranzer type
zbMATH Open document ID: 1270.35311
DOI: 10.1155/2013/958120
published in: Advances in Mathematical Physics
publication date: 2013-06-07T00:00:00Z
review text: Summary: This paper is devoted to the study of delta shock waves for a hyperbolic system of conservation laws of Keyfitz-Kranzer type with two linearly degenerate characteristics. The Riemann problem is solved constructively. The Riemann solutions include exactly two kinds. One consists of two (or just one) contact discontinuities, while the other contains a delta shock wave. Under suitable generalized Rankine-Hugoniot relation and entropy condition, the existence and uniqueness of delta shock solution are established. These analytical results match well the numerical ones. Finally, two kinds of interactions of elementary waves are discussed.
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 6171653
zbMATH Keywords: contact discontinuities
zbMATH Keywords: Rankine-Hugoniot relation
zbMATH Keywords: entropy condition
Wikidata QID: Q58918911
author: Hong Jun Cheng
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/958120
OpenAlex ID: W2047827853
cites work: A system of non-strictly hyperbolic conservation laws arising in elasticity theory
cites work: Existence of global bounded weak solutions to nonsymmetric systems of Keyfitz-Kranzer type
cites work: Resurrection of "Second Order" Models of Traffic Flow
cites work: Q4333357
cites work: Formation of $\delta$-Shocks and Vacuum States in the Vanishing Pressure Limit of Solutions to the Euler Equations for Isentropic Fluids
cites work: Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids
cites work: Riemann problem for the relativistic Chaplygin Euler equations
cites work: Delta shock waves in chromatography equations
cites work: Delta shock waves as limits of vanishing viscosity for 2-D steady pressureless isentropic flow
cites work: Delta shock wave formation in the case of triangular hyperbolic system of conservation laws
cites work: Dynamics of propagation and interaction of \(\delta\)-shock waves in conservation law systems
cites work: The two-dimensional Riemann problem for isentropic Chaplygin gas dynamic system
cites work: Q4282402
cites work: Spaces of weighted measures for conservation laws with singular shock solutions
cites work: Q4258266
cites work: \(\delta ^{\prime }\)-shock waves as a new type of solutions to systems of conservation laws
cites work: The Riemann problem admitting \(\delta-, \delta ^{\prime }\)-shocks, and vacuum states (the vanishing viscosity approach)
cites work: The Riemann problem for the transportation equations in gas dynamics
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: Riemann problems for a class of coupled hyperbolic systems of conservation laws
cites work: New developments of delta shock waves and its applications in systems of conservation laws
cites work: Q4258276
cites work: Non-oscillatory central differencing for hyperbolic conservation laws
description: scientific article; zbMATH DE number 6171653