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.
A note on the convergence of the solution of the high order Camassa-Holm equation to the entropy ones of a scalar conservation law / Coclite, Giuseppe Maria; di Ruvo, L.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - 37:3(2017), pp. 1247-1282. [10.3934/dcds.2017052]
A note on the convergence of the solution of the high order Camassa-Holm equation to the entropy ones of a scalar conservation law
COCLITE, Giuseppe Maria;
2017-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
