广义立方双色散方程解的渐近性质  

Asymptotic Behavior of the Solution for the Generalized Cubic Double Dispersion Equation

作　　者：孙明丽 刘亚成[2] 董晓璋[2] 

机构地区：[1]南京市聋人学校,南京210007 [2]哈尔滨工程大学理学院,哈尔滨150001

出　　处：《工程数学学报》2009年第3期567-570,共4页Chinese Journal of Engineering Mathematics

摘　　要：本文研究广义立方双色散方程的初边值问题,它包括了几类双色散方程以及Bq,IBq,IMBq方程作为特殊情形,当方程非线性项满足某些条件时,利用等价变换和改进的积分估计法证明了问题整体广义解按时间的指数形式衰减为零。最后,将本文定理结论应用到实际模型中,得到了问题的解具有衰减行为时方程参数应满足的条件。We study the initial boundary value problem of the generalized cubic double dispersion equation which includes double dispersion equations, Bq equations, IBq equations and IMBq equations as special cases. By using the equivalence transformation method and a development integral estimate method, we prove that the solution of the problem decay to zero exponentially with respect to time, when the nonlinear term satisfies certain conditions. Finally, as an application of our theorem, we obtain the condition that parameters of the equation should satisfy when the solution has the asymptotic behavior.

关 键 词：广义立方双色散方程 积分估计法 变换问题 整体广义解 渐近性质 

分 类 号：O175.29[理学—数学]