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Well-posedness and Continuity Properties of a generalized Degasperis-Procesi equation in $B^1_{\infty,1}$.
  • Shaohui Gui,
  • Min Li,
  • Shiping Zhong
Shaohui Gui
Gannan Normal University

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Min Li
Jiangxi University of Finance and Economics
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Shiping Zhong
Gannan Normal University
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Abstract

In this paper, we obtain the local-in-time existence and uniqueness of solution to the generalized Degasperis-Procesi equation in $B^1_{\infty,1}(\mathbb{R})$. Moreover, we prove that the data-to-solution of this equation is continuous but not uniformly continuous in $B^1_{\infty,1}(\mathbb{R})$