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Global Dissipative Solution for an Extended Dullin–Gottwald–Holm Equation

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  • Yan Wang
  • Yongsheng Yan
  • Rui Wu

Abstract

The current paper devotes to the continuation of the solutions for the Dullin–Gottwald–Holm equation with forcing. Due to forcing, this equation loses the conservation of energy and cannot be regarded as the Hamiltonian system. Thus, through employing the characteristic method and exploiting the balance law, we prove the existence of a semigroup of a global dissipative solution, which is defined for each initial value u0 ∈ H1(ℝ) and depends continuity on it.

Suggested Citation

  • Yan Wang & Yongsheng Yan & Rui Wu, 2022. "Global Dissipative Solution for an Extended Dullin–Gottwald–Holm Equation," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:3431899
    DOI: 10.1155/2022/3431899
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    References listed on IDEAS

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    1. Xi Tu & Zhaoyang Yin, 2018. "Global weak solutions for a generalized Camassa–Holm equation," Mathematische Nachrichten, Wiley Blackwell, vol. 291(16), pages 2457-2475, November.
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