We consider a shallow water equation of Camassa-Holm type, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solution of the dispersive equation converges to the unique entropy solution 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 solutions of the Camassa-Holm equation to the entropy ones of a scalar conservation law.

COCLITE, Giuseppe Maria;DI RUVO, LORENZO
2016-01-01

Abstract

We consider a shallow water equation of Camassa-Holm type, which contains nonlinear dispersive effects. We prove that as the diffusion parameter tends to zero, the solution of the dispersive equation converges to the unique entropy solution 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/139749
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