Bifurcation under parameter change of Riemann solutions for nonstrictly hyperbolic systems

DOI10.1007/s00033-014-0469-7zbMath1327.35030OpenAlexW1985823976MaRDI QIDQ493551

V. Matos, Arthur V. Azevedo, Jesus C. Da Mota, Dan Marchesin

Publication date: 3 September 2015

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-014-0469-7

zbMATH Keywords

Riemann problemsloss of hyperbolicitymultiphase flow in porous mediaoil-water-gas saturation trianglesolution equivalenceumbilic points

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Bifurcations in context of PDEs (35B32) PDEs in connection with geophysics (35Q86) Singular hyperbolic equations (35L81)

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Compositional flow in porous media: Riemann problem for three alkanes ⋮ On a universal structure for immiscible three-phase flow in virgin reservoirs ⋮ Resonance in rarefaction and shock curves: Local analysis and numerics of the continuation method

Cites Work

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• The Riemann problem for 2\(\times 2\) systems of hyperbolic conservation laws with case I quadratic nonlinearities
• Solution of the Riemann problem for a prototype 2\(\times 2\) system of non-strictly hyperbolic conservation laws
• A system of non-strictly hyperbolic conservation laws arising in elasticity theory
• A global formalism for nonlinear waves in conservation laws
• Stable hyperbolic singularities for three-phase flow models in oil reservoir simulation
• Supersonic flow and shock waves. Reprint of the ed. published by Interscience Publishers, New York
• Quadratic gradients on the plane are generically Morse-Smale
• The Riemann problem for materials with nonconvex equation of state. II: General flow
• Capillary instability in models for three-phase flow
• Structurally stable Riemann solutions
• Classification of homogeneous quadratic conservation laws with viscous terms
• RIEMANN SOLUTIONS FOR VERTICAL FLOW OF THREE PHASES IN POROUS MEDIA: SIMPLE CASES
• Hyperbolic systems of conservation laws II
• Geometry of Hugoniot curves in 2 × 2 systems of hyperbolic conservation laws with quadratic flux functions
• Transitional Waves for Conservation Laws
• LARGE VISCOUS SOLUTIONS FOR SMALL DATA IN SYSTEMS OF CONSERVATION LAWS THAT CHANGE TYPE
• Topological resolution of Riemann problems for pairs of conservation laws
• Riemann Problems for Nonstrictly Hyperbolic 2 × 2 Systems of Conservation Laws
• The classification of 2 × 2 systems of non-strictly hyperbolic conservation laws, with application to oil recovery
• Nonlinear Resonance in Systems of Conservation Laws
• The Riemann Problem Near a Hyperbolic Singularity: The Classification of Solutions of Quadratic Riemann Problems I
• The Riemann Problem Near a Hyperbolic Singularity II
• The Riemann Problem Near a Hyperbolic Singularity III
• Conservation Laws of Mixed Type Describing Three-Phase Flow in Porous Media
• The Riemann Problem for General 2 × 2 Conservation Laws
• Uniqueness of the Riemann Solution for Three-Phase Flow in a Porous Medium
• Some problems in the theory of quasilinear equations