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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 (1-∂x2)u0∈M+(R), u0 ∈ H1(R), and u0 ∈ L1(R), the existence and uniqueness of the global weak solution to the equation are shown to be true.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:840919
DOI: 10.1155/2012/840919
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