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**The local strong and weak solutions for a generalized Novikov equation.**
*(English)*
Zbl 1243.35044

Summary: The Kato theorem for abstract differential equations is applied to establish the local well-posedness of the strong solution for a nonlinear generalized Novikov equation in space \(C([0, T), H^s(\mathbb R)) \cap C^1([0, T), H^{s-1}(\mathbb R))\) with \(s > (3/2)\). The existence of weak solutions for the equation in the lower-order Sobolev space \(H^s(\mathbb R)\) with \(1 \leq s \leq (3/2)\) is acquired.

### MSC:

35G25 | Initial value problems for nonlinear higher-order PDEs |

35A01 | Existence problems for PDEs: global existence, local existence, non-existence |

35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |

35D30 | Weak solutions to PDEs |

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\textit{M. Wu} and \textit{Y. Zhong}, Abstr. Appl. Anal. 2012, Article ID 158126, 14 p. (2012; Zbl 1243.35044)

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### References:

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