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

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  • Yongsheng Mi
  • Chunlai Mu

Abstract

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.

Suggested Citation

  • Yongsheng Mi & Chunlai Mu, 2013. "Well‐Posedness, Blow‐Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two‐Component Camassa‐Holm Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:547261
    DOI: 10.1155/2013/547261
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    References listed on IDEAS

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    1. Weiguo Rui & Yao Long, 2012. "Integral Bifurcation Method together with a Translation‐Dilation Transformation for Solving an Integrable 2‐Component Camassa‐Holm Shallow Water System," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Weiguo Rui & Yao Long, 2012. "Integral Bifurcation Method together with a Translation-Dilation Transformation for Solving an Integrable 2-Component Camassa-Holm Shallow Water System," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-21, December.
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