Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
Volume 36, Issue 6, Pages 2981-2990Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2016.36.2981
Keywords
Singular limit; compensated compactness; Camassa-Holm equation; entropy condition
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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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