The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term

Ying Wang and YunXi Guo

Abstract and Applied Analysis, 2012, vol. 2012, 1-23

Abstract:

A shallow water wave equation with a weakly dissipative term, which includes the weakly dissipative Camassa-Holm and the weakly dissipative Degasperis-Procesi equations as special cases, is investigated. The sufficient conditions about the existence of the global strong solution are given. Provided that , and , the existence and uniqueness of the global weak solution to the equation are shown to be true.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:840919

DOI: 10.1155/2012/840919

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