Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux. I.

DOI10.1016/j.jde.2016.06.026zbMath1368.35176arXiv1512.04863OpenAlexW2962878220MaRDI QIDQ306224

Laura Caravenna, Stefano Bianchini, Giovanni Alberti

Publication date: 31 August 2016

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

Full work available at URL: https://arxiv.org/abs/1512.04863

zbMATH Keywords

Lagrangian descriptionEulerian formulation

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65) Dynamics induced by flows and semiflows (37C10) Initial value problems for first-order hyperbolic systems (35L45) Hyperbolic equations on manifolds (58J45)

Related Items (9)

Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux. I. ⋮ Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation ⋮ Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2 ⋮ A fast, robust, and simple Lagrangian-Eulerian solver for balance laws and applications ⋮ A class of Lagrangian-Eulerian shock-capturing schemes for first-order hyperbolic problems with forcing terms ⋮ A new finite volume approach for transport models and related applications with balancing source terms ⋮ Regularity estimates for continuous solutions of \(\alpha\)-convex balance laws ⋮ A directional Lipschitz extension lemma, with applications to uniqueness and Lagrangianity for the continuity equation ⋮ The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group

Cites Work

• Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux. I.
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• Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation
• Continuous solutions for balance laws
• Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group
• On rings of operators. Reduction theory
• Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs
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