Acta mathematica scientia, Series B >
PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION
Received date: 2005-12-20
Revised date: 2007-03-01
Online published: 2008-07-20
In this article, the existence, uniqueness and regularities of the global generalized 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.
Chen Guowang , Xue Hongxia . PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION[J]. Acta mathematica scientia, Series B, 2008 , 28(3) : 573 -587 . DOI: 10.1016/S0252-9602(08)60060-0
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