| 一类广义KdV－Burgers型方程的初边值问题 |
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| 引用本文： | 尚亚东.一类广义KdV－Burgers型方程的初边值问题[J].应用数学,1996(2). |
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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 |
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| 摘 要： | 本文研究了一类带三阶粘性项的广义ＫｄＶ－Ｂｕｒｇｅｒｓ型方程的初边值问题．运用Ｇａｌｅｒｋｉｎ逼近方法，结合能量估计，得到了问题整体解的存在性，正则性，唯一性和稳定性等结果．并在一定条件下讨论了问题的解的渐近行为和“爆破”现象．
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| 关 键 词： | KdV－Burgers方程 初边值问题 整体解 Galerkin方法 能量估计 渐近行为 爆破 |
Initial Boundary Value Problem for a Class of the Generalized KdV-Burgers Type Equations |
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| Shang Yadong.Initial Boundary Value Problem for a Class of the Generalized KdV-Burgers Type Equations[J].Mathematica Applicata,1996(2). |
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| Authors: | Shang Yadong |
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| Abstract: | This paper considers the initial-boundary value problem for the generalized KdV-Burgers equations with the third order viscous term. The existence and uniqueness of the global solution for the problem are proved by means of a priority estimation and the Galerkinmethod. The asymptotic behavior and "blow up" Phenomenon of the solution for the problem are inverstigated under certain conditions. |
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| Keywords: | KdV-Burgers equation Initial-boundary value problem Global solution Galerkin method Energy estimation Asymptotic behavior Blow up |
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