| 一类四阶非线性波动方程组的初边值问题 |
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| 引用本文： | 欧阳苗. 一类四阶非线性波动方程组的初边值问题[J]. 厦门理工学院学报, 2014, 0(1): 107-111 |
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| 作者姓名： | 欧阳苗 |
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| 作者单位： | 厦门理工学院应用数学学院,福建厦门361024 |
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| 摘 要： | 四阶非线性波动方程组utt-uxx-uxxt-uxxtt=f(ut)+g(u)(0≤x≤1,0≤t≤T)表示多条粘弹性杆耦合振动时,不仅考虑由外力f(ut)产生的纵向形变波,还考虑不同外力相互作用产生的非线性项g(u).采用Glerkin方法对其第一边值问题证明了整体强解的存在性和唯一性.
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| 关 键 词： | 非线性波动方程组 初边值 整体强解 |
Initial Boundary Value Problems for 4th-order Nonlinear Wave Equations |
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| OUYANG Miao. Initial Boundary Value Problems for 4th-order Nonlinear Wave Equations[J]. Journal of Xiamen University of Technology, 2014, 0(1): 107-111 |
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| Authors: | OUYANG Miao |
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| Affiliation: | OUYANG Miao ( School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China) |
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| Abstract: | In expressing elastic rods coupled vibration, the fourth order nonlinear wave equations utt-uxx-uxxt-uxxtt=f（ut）＋g（u）（0≤x≤1,0≤t≤T） does not only consider the vertical deformation wave from forces f（u,） , but also the nonlinear term g（u） under interactive forces. By means of Galerkin method, the existence and uniqueness of global strong solution to the initial boundary value problem is obtained. |
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| Keywords: | nonlinear wave equations initial boundary value problem global strong solution |
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