The relative entropy method for the stability of intermediate shock waves; the rich case

DOI10.3934/dcds.2016.36.4569zbMath1347.35169OpenAlexW2313966439MaRDI QIDQ262123

Denis Serre, Alexis F. Vasseur

Publication date: 29 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2016.36.4569

zbMATH Keywords

hyperbolic conservation lawsentropy methodrich systems

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Stability in context of PDEs (35B35) Hyperbolic conservation laws (35L65)

Related Items (11)

Contraction property for large perturbations of shocks of the barotropic Navier-Stokes system ⋮ Uniqueness and stability of entropy shocks to the isentropic Euler system in a class of inviscid limits from a large family of Navier-Stokes systems ⋮ Well-posedness of the Riemann problem with two shocks for the isentropic Euler system in a class of vanishing physical viscosity limits ⋮ A review of recent applications of the relative entropy method to discontinuous solutions of conservation laws ⋮ Contraction for large perturbations of traveling waves in a hyperbolic–parabolic system arising from a chemotaxis model ⋮ Stability and Uniqueness for Piecewise Smooth Solutions to a Nonlocal Scalar Conservation Law with Applications to Burgers--Hilbert Equation ⋮ Finite time stability for the Riemann problem with extremal shocks for a large class of hyperbolic systems ⋮ \(L^2\)-type contraction for shocks of scalar viscous conservation laws with strictly convex flux ⋮ Uniqueness of a planar contact discontinuity for 3D compressible Euler system in a class of zero dissipation limits from Navier-Stokes-Fourier system ⋮ On uniqueness of solutions to conservation laws verifying a single entropy condition ⋮ Localised relative energy and finite speed of propagation for compressible flows

Cites Work

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• \(L^2\)-type contraction for systems of conservation laws
• Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non-\(BV\) perturbations
• \(L ^{2}\) stability estimates for shock solutions of scalar conservation laws using the relative entropy method
• The structure of dissipative viscous system of conservation laws
• Semi-linear and kinetic relaxation for systems of conservation laws
• Alternate Evans Functions and Viscous Shock Waves
• Hyperbolic systems of conservation laws II
• The existence of multidimensional shock fronts
• The stability of multidimensional shock fronts
• Long-time stability in systems of conservation laws, using relative entropy/energy

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