An extension of Glimm's method to inhomogeneous strictly hyperbolic systems of conservation laws by ``weaker than weak solutions of the Riemann problem

DOI10.1016/j.jde.2005.06.016zbMath1093.35048OpenAlexW1967161947MaRDI QIDQ818489

John M. Hong

Publication date: 20 March 2006

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2005.06.016

zbMATH Keywords

weak solutionsRiemann problemhyperbolic systems of conservation lawsGlimm's methodLax technique

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Initial value problems for first-order hyperbolic systems (35L45)

Related Items

Global Transonic Solutions of Planetary Atmospheres in a Hydrodynamic Region---Hydrodynamic Escape Problem Due to Gravity and Heat ⋮ Global bounded variation solutions describing Fanno–Rayleigh fluid flows in nozzles ⋮ Globally Lipschitz continuous solutions to a class of quasilinear wave equations ⋮ Global classical solutions near vacuum to the initial-boundary value problem of isentropic flows through divergent ducts ⋮ Global entropy solutions to a class of quasi-linear wave equations with large time-oscillating sources ⋮ Existence and uniqueness of generalized stationary waves for viscous gas flow through a nozzle with discontinuous cross section ⋮ The initial-boundary value problem of hyperbolic integro-differential systems of nonlinear balance laws ⋮ Global existence of solutions for a nonstrictly hyperbolic system ⋮ Global solutions for initial-boundary value problem of quasilinear wave equations ⋮ A sign matrix based scheme for non-homogeneous PDE's with an analysis of the convergence stagnation phenomenon ⋮ Concentration of source terms in generalized Glimm scheme for global entropy solutions of nonlinear hyperbolic balance laws ⋮ On the generalized Buckley-Leverett equation ⋮ Formation of Delta Standing Wave for a Scalar Conservation Law with a Linear Flux Function Involving Discontinuous Coefficients ⋮ Smooth and discontinuous junctions in the \(p\)-system ⋮ A robust and entropy-satisfying numerical scheme for fluid flows in discontinuous nozzles ⋮ Generalized Glimm scheme to the initial boundary value problem of hyperbolic systems of balance laws ⋮ The generalized Buckley-Leverett and the regularized Buckley-Leverett equations ⋮ Hamiltonian regularisation of shallow water equations with uneven bottom

Cites Work

• Unnamed Item
• Unnamed Item
• Quasilinear hyperbolic systems
• The Riemann problem for a class of resonant hyperbolic systems of balance laws
• Global solution of the Cauchy problem for a class of 2x2 nonstrictly hyperbolic conservation laws
• The generic solution of the Riemann problem in a neighborhood of a point of resonance for systems of nonlinear balance laws
• Definition and weak stability of nonconservative products
• Hyperbolic systems of conservation laws II
• Existence theory for nonlinear hyperbolic systems in nonconservative form
• Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form
• A Bound on the Total Variation of the Conserved Quantities for Solutions of a General Resonant Nonlinear Balance Law
• Convergence of the $2 \times 2$ Godunov Method for a General Resonant Nonlinear Balance Law
• Solutions in the large for nonlinear hyperbolic systems of equations