A note on the convergence of the solutions of the Camassa-Holm equation to the entropy ones of a scalar conservation law

DOI10.3934/dcds.2016.36.2981zbMath1336.35056OpenAlexW4248573216MaRDI QIDQ255894

Giuseppe Maria Coclite, Lorenzo di Ruvo

Publication date: 9 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.2016.36.2981

zbMATH Keywords

shallow water equationsingular limitcompensated compactnessentropy conditionnonlinear dispersive effects

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Hyperbolic conservation laws (35L65) Initial value problems for nonlinear higher-order PDEs (35G25)

Related Items (13)

On the convergence of the modified Rosenau and the modified Benjamin-Bona-Mahony equations ⋮ A note on convergence of the solutions of Benjamin-Bona-Mahony type equations ⋮ On \(H^2\)-solutions for a Camassa-Holm type equation ⋮ Energy conservation and well-posedness of the Camassa-Holm equation in Sobolev spaces ⋮ On the classical solutions for the high order Camassa-Holm type equations ⋮ On a Hamiltonian regularization of scalar conservation laws ⋮ Infinite propagation speed and asymptotic behavior for a generalized fifth-order Camassa–Holm equation ⋮ An asymptotic property of the Camassa-Holm equation on the half-line ⋮ Convergence of the Kuramoto-Sinelshchikov equation to the Burgers one ⋮ A note on the convergence of the solution of the high order Camassa-Holm equation to the entropy ones of a scalar conservation law ⋮ Transfer of energy in Camassa-Holm and related models by use of nonunique characteristics ⋮ Singular limits with vanishing viscosity for nonlocal conservation laws ⋮ CONVERGENCE OF THE SOLUTIONS ON THE GENERALIZED KORTEWEG–DE VRIES EQUATION∗

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