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Asymptotics for the Ostrovsky-Hunter Equation in the Critical Case

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  • Fernando Bernal-Vílchis
  • Nakao Hayashi
  • Pavel I. Naumkin

Abstract

We consider the Cauchy problem for the Ostrovsky-Hunter equation , ,   , , where . Define . Suppose that is a pseudodifferential operator with a symbol such that , , and . For example, we can take . We prove the global in time existence and the large time asymptotic behavior of solutions.

Suggested Citation

  • Fernando Bernal-Vílchis & Nakao Hayashi & Pavel I. Naumkin, 2017. "Asymptotics for the Ostrovsky-Hunter Equation in the Critical Case," International Journal of Differential Equations, Hindawi, vol. 2017, pages 1-21, January.
    • Handle: RePEc:hin:jnijde:3879017
    DOI: 10.1155/2017/3879017
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