A remark on the uniqueness of solutions to hyperbolic conservation laws

DOI10.1007/s00205-023-01936-yarXiv2305.17203OpenAlexW4388105124MaRDI QIDQ6091830

Alberto Bressan, Camillo De Lellis

Publication date: 27 November 2023

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.17203

zbMATH Keywords

vanishing viscosity approximationsLipschitz semigroup of weak solutions

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Hyperbolic conservation laws (35L65) Initial value problems for first-order hyperbolic systems (35L45) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• The entropy condition and the admissibility of shocks
• Oleinik type estimates and uniqueness for \(n \times n\) conservation laws
• Uniqueness of weak solutions to systems of conservation laws
• On the Riemann problem for non-conservative hyperbolic systems
• A uniqueness condition for hyperbolic systems of conservation laws.
• \(L^1\) stability estimates for \(n\times n\) conservation laws
• The unique limit of the Glimm scheme
• Vanishing viscosity solutions of nonlinear hyperbolic systems
• Rectifiable sets, densities and tangent measures
• Uniqueness and weak-BV stability for \(2\times 2\) conservation laws
• Well-posedness of the Cauchy problem for 𝑛×𝑛 systems of conservation laws
• The Riemann Problem for General 2 × 2 Conservation Laws
• Hyperbolic Conservation Laws in Continuum Physics
• Front tracking for hyperbolic conservation laws
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