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

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

数学物理学报(英文版)

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

陈国旺; 薛红霞

郑州大学数学系, 郑州 450052

收稿日期:2005-12-20 修回日期:2007-03-01 出版日期:2008-07-20 发布日期:2008-07-20
通讯作者: 陈国旺
基金资助:
Sponsored by the NNSFC (10671182)

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

摘要/Abstract

摘要：

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.

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

Abstract:

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

中图分类号:

35L30

陈国旺; 薛红霞. PERIODIC BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM OF THE GENERALIZED CUBIC DOUBLE DISPERSION EQUATION[J]. 数学物理学报(英文版), 2008, 28(3): 573-587.

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

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

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