| 带三阶粘性项的高维广义KdV—Burgers型方程组的整体解 |
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| 引用本文： | 尚亚东.带三阶粘性项的高维广义KdV—Burgers型方程组的整体解[J].甘肃科学学报,1996,8(2):1-9. |
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| 作者姓名： | 尚亚东 |
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| 作者单位： | 西安石油学院基础部 |
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| 摘 要： | 考虑了一类带三阶粘性项的高维广义ＫｄＶ－Ｂｕｒｇｅｒｓ型方程组的周期边值问题和初值问题，利用先验估计及Ｇａｌｅｒｋｉｎ方法，证明了所论问题整体解的存在性、唯一性和正则性。
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| 关 键 词： | 周期边值问题 整体解 KdV－B方程 非线性波动 |
THE GLOBAL SOLUTION OF THE SYSTEM OF MULTIDIMENSIONAL GENERALIZED KDV-BURGERS EQUATIONS WITH THIRD ORDER VISCOUS TERM |
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| SHANG Yadong.THE GLOBAL SOLUTION OF THE SYSTEM OF MULTIDIMENSIONAL GENERALIZED KDV-BURGERS EQUATIONS WITH THIRD ORDER VISCOUS TERM[J].Journal of Gansu Sciences,1996,8(2):1-9. |
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| Authors: | SHANG Yadong |
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| Abstract: | This paper deals with the periodic boundary value problem and the initial value problem for the system of multidimensional generalized KdV-Burgers equations with third order viscous term.The existence and uniqueness of the global solution for these problems are proved by the Galerkin method and a priori estimation.The asymptotic behaviour of the solution for the problem is investigated under certain conditions.The sufficient conditions are given for the existence of the blowing-up solution for a class of systems of multidimensional inhomogeneous generalized KdV-Burgers equations. |
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| Keywords: | KdV-Burgers equation BBM-Burgers equation Periodic boundary value problem Initial value problem Global solution Galerkin method Asymptotic behavior Blow up |
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