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Cauchy problem of generalized Boussinesq equation with combined power‐type nonlinearities
Author(s) -
Runzhang Xu
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1536
Subject(s) - mathematics , initial value problem , cauchy problem , type (biology) , cauchy distribution , power (physics) , mathematical analysis , physics , geology , quantum mechanics , paleontology
In this paper, we study the Cauchy problem of generalized Boussinesq equation with combined power‐type nonlinearities u tt − u xx + u xxxx + f ( u ) xx = 0, where f ( u ) = ∑ k = 1 la k | u |p k − 1 u or∑ k = 1 la k | u |p k − 1 u − ∑ j = 1 mb j | u |q j − 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. Copyright © 2011 John Wiley & Sons, Ltd.