PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION |
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| Authors: | Chen Guowang Xue Hongxia |
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| Institution: | [1]Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China [2]Department of Mathematics and Physics, Zhengzhou Institute of Aeronautical Industry Management, Zhengzhou 450015, China |
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| Abstract: | In this article, the existence, uniqueness and regularities of the global gener-alized solution and global classical solution for the periodic boundary value problem and the Cauchy problem of the general cubic double dispersion equation utt -uxx-auxxtt bux4 - duxxt= f(u)xx are proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given. |
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| Keywords: | The generalized cubic double dispersion equation Cauchy problem exis-tence and uniqueness of global solution nonexistence of global solution |
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