Abstract
In this paper, we study the Cauchy problem of generalized Boussinesq equation with combined power-type nonlinearities utt −uxx + uxxxx + f(u)xx = 0, where or . 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.
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