Journal of Applied Mathematics (Jan 2013)

Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation

  • Yongsheng Mi,
  • Chunlai Mu

DOI
https://doi.org/10.1155/2013/547261
Journal volume & issue
Vol. 2013

Abstract

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We study the Cauchy problem of a weakly dissipative modified two-component Camassa-Holm equation. We firstly establish the local well-posedness result. Then we present a precise blow-up scenario. Moreover, we obtain several blow-up results and the blow-up rate of strong solutions. Finally, we consider the asymptotic behavior of solutions.