| Burgers方程与高阶Burgers方程的非线性边-初值问题 |
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| 引用本文： | 王明亮.Burgers方程与高阶Burgers方程的非线性边-初值问题[J].兰州大学学报(自然科学版),1990(2). |
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| 作者姓名： | 王明亮 |
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| 作者单位： | 兰州大学数学系 |
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| 摘 要： | 本文借助 Cole-Hopf 变换求出了 Burgers 方程在有限区间和半无限直线上非线性边-初值问题的准确解,证明了高阶 Bursers 方程的线性与非线性边-初值问题的解,都可借助相应的线性问题的解来表示,还讨论了非线性边-初值问题解的唯一性.
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| 关 键 词： | 非线性边-初值问题 解 唯一性 Burgers 和高阶 Burgers 方程 |
Nonlinear Boundary-Initial Value Problems for the Burgers Equation and the Higher Order Burgers Equation |
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| Wang Mingliang.Nonlinear Boundary-Initial Value Problems for the Burgers Equation and the Higher Order Burgers Equation[J].Journal of Lanzhou University(Natural Science),1990(2). |
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| Authors: | Wang Mingliang |
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| Institution: | Department of Mathematics |
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| Abstract: | In the present paper,exact solutions to nonlinear boundary-initial,valueproblems for the Burgers equation in a finite interval and a half-infinitestraight line are given with the aid of Cole-Hopf transformation.It isproved that solutions to linear and nonlinear boundary-initial value problemsfor the higher order Burgers equation can be represented by solutions ofcorresponding linear problems.The uniqueness of the solution to nonlinearboundary-initial value problems for both Burgers equation and higherorder Burgers equation is discussed. |
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| Keywords: | nonlinear boundary-initial value problems solutions uniqueness Burgers and higher order Burgers equations |
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