On uniqueness of solutions to conservation laws verifying a single entropy condition

DOI10.1142/S0219891619500061zbMath1453.35122arXiv1709.05610WikidataQ127822894 ScholiaQ127822894MaRDI QIDQ5237474

Sam G. Krupa, Alexis F. Vasseur

Publication date: 18 October 2019

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

Full work available at URL: https://arxiv.org/abs/1709.05610

zbMATH Keywords

scalar conservation lawsrelative entropiesKruzhkov entropy solutionsstrictly convex flux functionOleĭnik condition

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (11)

Generalized characteristics for finite entropy solutions of Burgers' equation ⋮ On the \(L^2\) stability of shock waves for finite-entropy solutions of Burgers ⋮ Nonuniqueness and existence of continuous, globally dissipative Euler flows ⋮ The rectifiability of the entropy defect measure for Burgers equation ⋮ Uniqueness and weak-BV stability for \(2\times 2\) conservation laws ⋮ A review of recent applications of the relative entropy method to discontinuous solutions of conservation laws ⋮ Minimal entropy conditions for scalar conservation laws with general convex fluxes ⋮ Sharp a-contraction estimates for small extremal shocks ⋮ 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

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