Riemann problem for a geometrical optics system

DOI10.1007/s10114-014-3561-1zbMath1307.35167OpenAlexW2042840194MaRDI QIDQ477872

Hong Jun Cheng, Han-Chun Yang

Publication date: 10 December 2014

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-014-3561-1

zbMATH Keywords

vacuumconvex hullcontact discontinuitiesentropy conditiondelta shock wavegeneralized Rankine-Hugoniot relations

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Initial value problems for first-order hyperbolic systems (35L45) Degenerate hyperbolic equations (35L80) Geometric optics (78A05)

Related Items (6)

Flux approximation to the isentropic relativistic Euler equations ⋮ The perturbed Riemann problem for a geometrical optics system ⋮ Delta‐shock for a class of systems of conservation laws of the Keyfitz–Kranzer type ⋮ Delta shock waves as flux-approximation limit of solutions to the modified Chaplygin gas equations ⋮ Delta shock waves with Dirac delta function in both components for systems of conservation laws ⋮ Concentration in vanishing pressure limit of solutions to the modified Chaplygin gas equations

Cites Work

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• New developments of delta shock waves and its applications in systems of conservation laws
• The Riemann problem admitting \(\delta-, \delta ^{\prime }\)-shocks, and vacuum states (the vanishing viscosity approach)
• Non-oscillatory central differencing for hyperbolic conservation laws
• Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws
• Two-dimensional Riemann problem for a hyperbolic system of nonlinear conservation laws. I: Four-\(J\) cases
• Existence and uniqueness of discontinuous solutions defined by Lebesgue-Stieltjes integral
• Riemann problems for a class of coupled hyperbolic systems of conservation laws
• Multi-phase computations in geometrical optics
• The Riemann problem for the transportation equations in gas dynamics

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