Open AccessA 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 - 2017
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