PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION

doi:10.1016/S0252-9602(08)60060-0

Acta mathematica scientia,Series B

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PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION

Chen Guowang; Xue Hongxia

Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China

Received:2005-12-20 Revised:2007-03-01 Online:2008-07-20 Published:2008-07-20
Contact: Chen Guowang

Abstract

Abstract:

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
u_tt-u_xx-au_xxtt+bu_x⁴-du_xxt=f(u)_xx
are proved, and the sufficient conditions of blow-up of the solutions for the Cauchy problems in finite time are given.

Key words: The generalized cubic double dispersion equation, Cauchy problem, existence and uniqueness of global solution, nonexistence of global solution

CLC Number:

35L30

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.

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PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION

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