The Riemann problem for a class of conservation laws of mixed type

DOI10.1016/0022-0396(82)90103-6zbMath0465.35063OpenAlexW2031313153MaRDI QIDQ1154610

Michael Shearer

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0022-0396(82)90103-6

zbMATH Keywords

phase transitionsRiemann problemMaxwell equal area rulestationary shock wavesinitial step data

Mathematics Subject Classification ID

Related Items (31)

Thermo-elastic aspects of dynamic nucleation ⋮ Riemann problem in non-ideal gas dynamics ⋮ Dynamics of propagating phase boundaries: Adiabatic theory for thermoelastic solids ⋮ The Riemann problem for thermoelastic materials with phase change ⋮ The Riemann problem for a van der Waals fluid with entropy rate admissibility criterion-isothermal case ⋮ Traveling waves in a relaxation system ⋮ Fine phase mixtures in one-dimensional non-convex elastodynamics ⋮ The Riemann problem for a system of conservation laws of mixed type with a cubic nonlinearity ⋮ Change of type in three-phase flow: A simple analogue ⋮ The Riemann problem for a class of nonlinear degenerate equations ⋮ The numerical and analytical solution of ill-posed systems of conservation laws ⋮ Thermal trapping and kinetics of martensitic phase boundaries ⋮ Two-phase solutions for one-dimensional non-convex elastodynamics ⋮ The Riemann problem for van der Waals fluids with nonclassical phase transitions ⋮ Non-consistency of Glimm's scheme for the elastic string system ⋮ A Consistency Study of Coarse-Grained Dynamical ChainsthroughaNonlinearWaveEquationofMixed Type ⋮ High-order entropy-conservative schemes and kinetic relations for van der Waals fluids ⋮ The Uniqueness and Stability of the Solution of the Riemann Problem of a System of Conservation Laws of Mixed Type ⋮ Uniqueness of admissible solutions of the Riemann problem for a system of conservation laws of mixed type ⋮ Characterization of Riemann Solvers for the Two Phasep-System ⋮ A free-Lagrange augmented Godunov method for the simulation of elastic-plastic solids. ⋮ Existence and Uniqueness of the Riemann Problem for a Nonlinear System of Conservation Laws of Mixed Type ⋮ The Riemann problem and the existence of weak solutions to a system of mixed-type in dynamic phase transition ⋮ Undercompressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity ⋮ EXISTENCE OF SOLUTIONS WITH MOVING PHASE BOUNDARIES IN THERMOELASTICITY ⋮ Kinetics and nucleation for driven thin film flow ⋮ Admissible Riemann solvers for genuinely nonlinear \(p\)-systems of mixed type ⋮ Numerical solution of a virtual internal bond model for material fracture ⋮ Visco-elastic relaxation with a van der Waals type stress ⋮ The Riemann problem for a nonlinear non-strictly hyperbolic system arising in biology ⋮ Diffusive-dispersive traveling waves and kinetic relations. I: Nonconvex hyperbolic conservation laws

Cites Work

• The Riemann problem for a class of hyperbolic conservation laws exhibiting a parabolic degeneracy
• The propagation of phase boundaries in elastic bars
• Systems of conservation laws of mixed type
• Admissibility criteria for propagating phase boundaries in a van der Waals fluid
• Global solutions for an extended class of hyperbolic systems of conservation laws
• The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity
• The entropy rate admissibility criterion for solutions of hyperbolic conservation laws
• The Riemann problem for materials with nonconvex equations of state. I: Isentropic flow
• Hyperbolic systems of conservation laws II
• The Riemann Problem for General 2 × 2 Conservation Laws
• Viscosity matrices for two‐dimensional nonlinear hyperbolic systems

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