Cauchy problem of generalized Boussinesq equation with combined power‐type nonlinearities |
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| Authors: | Xu Runzhang |
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| Institution: | 1. College of Science, Harbin Engineering University, , Harbin, 150001 China;2. Differential Equations Research Center, Harbin Engineering University, , Harbin, 150001 China |
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| 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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| Keywords: | generalized Boussinesq equations Cauchy problem global solution blow up |
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