Stability and Uniqueness for Piecewise Smooth Solutions to a Nonlocal Scalar Conservation Law with Applications to Burgers--Hilbert Equation

DOI10.1137/19M1257883zbMath1453.35123arXiv1904.09468WikidataQ114847142 ScholiaQ114847142MaRDI QIDQ5119976

Sam G. Krupa, Alexis F. Vasseur

Publication date: 9 September 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.09468

zbMATH Keywords

Hilbert transformweak entropy solutionsnonlocal sourcescalar balance lawsrelative entropiesBurgers-Hilbert equationsingle entropy condition

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Shocks and singularities for hyperbolic equations (35L67) Stability in context of PDEs (35B35) First-order nonlinear hyperbolic equations (35L60) Weak solutions to PDEs (35D30) Initial value problems for first-order hyperbolic equations (35L03)

Related Items

Generalized characteristics for finite entropy solutions of Burgers' equation ⋮ On the \(L^2\) stability of shock waves for finite-entropy solutions of Burgers ⋮ On the approximation of vorticity fronts by the Burgers–Hilbert equation ⋮ Highest cusped waves for the Burgers-Hilbert equation ⋮ Stability of traveling waves for the Burgers-Hilbert equation ⋮ Sharp a-contraction estimates for small extremal shocks ⋮ Finite time stability for the Riemann problem with extremal shocks for a large class of hyperbolic systems ⋮ Lipschitz continuity of solutions to drift-diffusion equations in the presence of nonlocal terms

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