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Cauchy problem of generalized Boussinesq equation with combined power-type nonlinearities

✍ Scribed by Xu Runzhang

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 181 KB
Volume: 34
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1536

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✦ Synopsis

In this paper, we study the Cauchy problem of generalized Boussinesq equation with combined power-type nonlinearities u tt u xx C u xxxx C f .u/ xx D 0, where f .u/ D P l kD1 a k juj pk 1 u or P l kD1 a k juj pk 1 u P m jD1 b j juj qj 1 u. The arguments powered by potential well method combined with some other analysis skills allow us to give the sharp conditions of global well-posedness. And we also characterize the blow-up phenomenon.

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