| Asymptotic Behavior of Solutions to the Generalized BBM-Burgers Equation |
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| 作者姓名： | Mi-na Jiang~ Yan-ling Xu~ Laboratory of Nonlinear Analysis |
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| 作者单位： | Mi-na Jiang~1，Yan-ling Xu~2 1 Laboratory of Nonlinear Analysis，Department of Mathematics，Central China Normal University，Wuhan 430079，China 2 Department of Information and Computer Science，College of Science，Huazhong Agriculture University，Wuhan 430079，China |
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| 基金项目： | Supported by the National Natural Science Foundation of China (No.10171037, No. 10401012) |
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| 摘 要： | We investigate the asymptotic behavior of solutions of the initial-boundary value problem for the generalized BBM-Burgers equation u_t f(u)_x=u_(xx) u_(xx) on the half line with the conditions u(0, t)=, u-, u(∞,t)=u_ and, u_-
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| 关 键 词： | 渐近性质 解 边值问题 广义BBM-Burgers微分方程 稀疏波动 |
| 收稿时间： | 25 June 2002 |
Asymptotic Behavior of Solutions to the Generalized BBM-Burgers Equation |
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| Mi-na Jiang,Yan-ling Xu Laboratory of Nonlinear Analysis,.Asymptotic Behavior of Solutions to the Generalized BBM-Burgers Equation[J].Acta Mathematicae Applicatae Sinica,2005,21(1):31-42. |
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| Authors: | Mi-na Jiang Yan-ling Xu |
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| Institution: | (1) Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, China;(2) Department of Information and Computer Science, College of Science, Huazhong Agriculture University, Wuhan 430079, China |
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| Abstract: | Abstract
We investigate the asymptotic behavior of solutions of the initial-boundary value problem for the generalized BBM-Burgers
equation u
t
+ f(u)
x
= u
xx
+ u
xxt
on the half line with the conditions u(0, t) = u
−, u(∞, t) = u
+ and u
− < u
+, where the corresponding Cauchy problem admits the rarefaction wave as an asymptotic states. In the present problem, because
of the Dirichlet boundary, the asymptotic states are divided into five cases depending on the signs of the characteristic
speeds f′(u
±) of boundary state u
− = u(0) and the far fields states u
+ = u(∞). In all cases both global existence of the solution and asymptotic behavior are shown under the smallness conditions.
Supported by the National Natural Science Foundation of China (No.10171037, No.10401012) |
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| Keywords: | BBM-Burgers equation stationary solution rarefaction wave a prioriestimate L~2-energy method |
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