A note on the convergence of the solution of the high order Camassa-Holm equation to the entropy ones of a scalar conservation law | Zendy

Giuseppe Maria Coclite | Zendy; Lorenzo di Ruvo | Zendy

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

Author(s) -

Giuseppe Maria Coclite,

Lorenzo di Ruvo

Publication year - 2016

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2017052

Subject(s) - conservation law , mathematics , entropy (arrow of time) , a priori and a posteriori , scalar (mathematics) , camassa–holm equation , mathematical analysis , mathematical physics , physics , thermodynamics , integrable system , philosophy , geometry , epistemology

We consider the high order Camassa-Holm equation, which is a non linear dispersive equation of the fifth order. We prove that as the diffusion and dispersion parameters tends to zero, the solutions converge to the entropy ones of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the $L^p$ setting

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