| 带一般边界BBM-Burgers方程强边界层解的稳定性 |
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| 引用本文： | 陈琴,刘艳.带一般边界BBM-Burgers方程强边界层解的稳定性[J].哈尔滨商业大学学报(自然科学版),2012(2):205-209. |
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| 作者姓名： | 陈琴 刘艳 |
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| 作者单位： | 暨南大学数学系 |
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| 基金项目： | 国家自然科学基金资助项目(10871082) |
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| 摘 要： | 研究带一般边界条件的广义BBM-Burgers方程ut-utxx-uxx+f(u)x=0的初边值问题边界层解的非线性稳定性,其边界条件为u(t,0)=ub(t)→ub(t→+∞),初始值u(0,x)=u0(x)→u+(x→+∞)(u+≠ub).在f″(u)>0,φx(x)<0,f’(ub)<0的条件下,用L2-能量方法证明其强边界层解具有非线性稳定性,从而澄清一般边界条件对边界层解的稳定性的影响.
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| 关 键 词： | 广义BBM-Burgers方程 边界层解 L2-能量方法 非线性稳定性 |
Stability of strong boundary layer solution for BBM-Burgers equation with a general boundary effect |
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| CHEN Qin,LIU Yan.Stability of strong boundary layer solution for BBM-Burgers equation with a general boundary effect[J].Journal of Harbin University of Commerce :Natural Sciences Edition,2012(2):205-209. |
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| Authors: | CHEN Qin LIU Yan |
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| Institution: | (Department of Mathematic,Jinan University,Guangzhou 510632,China) |
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| Abstract: | This paper is concerned with the nonlinear stability of boundary layer solution for general initial-boundary value problem for generalized BBM-Burgers equation ut-utxx-uxx+f(u)x=0 with the general boundary condition u(t,0)=ub(t)→ub(t→+∞) and the initial data u(0,x)=u0(x)→u+(x→+∞)(u+≠ub).Under the condition that f ″(u)>0,φx(x)<0 and f ′(ub)<0,the strong boundary layer solution for the above initial-boundary value problem has nonlinear stability by means of an L2-energy method were proved.And clarified the effect of the general boundary data on the stability of boundary layer solution. |
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| Keywords: | generalized BBM-Burgers equation boundary layer solution L2-energy method nonlinear stability |
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