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**The local strong and weak solutions for a generalized pseudoparabolic equation.**
*(English)*
Zbl 1246.35113

Summary: The Cauchy problem for a nonlinear generalized pseudoparabolic equation is investigated. The well-posedness of local strong solutions for the problem is established in the Sobolev space \(C([0, T); H^s(\mathbb R)) \bigcap C^1([0, T); H^{s-1}(\mathbb R))\) with \(s > 3/2\), while the existence of local weak solutions is proved in the space \(H^s(\mathbb R)\) with \(1 \leq s \leq 3/2\). Further, under certain assumptions of the nonlinear terms in the equation, it is shown that there exists a unique global strong solution to the problem in the space \(C([0, \infty); H^s(\mathbb R)) \bigcap C^1([0, \infty); H^{s-1}(\mathbb R))\) with \(s \geq 2\).

### MSC:

35K70 | Ultraparabolic equations, pseudoparabolic equations, etc. |

35K15 | Initial value problems for second-order parabolic equations |

35K55 | Nonlinear parabolic equations |

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\textit{N. Li}, Abstr. Appl. Anal. 2012, Article ID 568404, 12 p. (2012; Zbl 1246.35113)

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### References:

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