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Initial Boundary Value Problem and Asymptotic Stabilization of the Two‐Component Camassa‐Holm Equation

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  • Xiju Zong
  • Xingong Cheng
  • Zhonghua Wang
  • Zhenlai Han

Abstract

The nonhomogeneous initial boundary value problem for the two‐component Camassa‐Holm equation, which describes a generalized formulation for the shallow water wave equation, on an interval is investigated. A local in time existence theorem and a uniqueness result are achieved. Next by using the fixed‐point technique, a result on the global asymptotic stabilization problem by means of a boundary feedback law is considered.

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Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:635851
DOI: 10.1155/2011/635851
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