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

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  • Ying Wang
  • YunXi Guo

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.

Suggested Citation

  • Ying Wang & YunXi Guo, 2012. "The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-23, May.
    • Handle: RePEc:hin:jnlaaa:840919
    DOI: 10.1155/2012/840919
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