| 一类非线性弹性梁方程弱解存在的唯一性 |
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| 引用本文： | 闫思青,张建文.一类非线性弹性梁方程弱解存在的唯一性[J].太原理工大学学报,2007,38(1):91-94. |
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| 作者姓名： | 闫思青 张建文 |
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| 作者单位： | 太原理工大学,理学院,山西,太原,030024 |
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| 摘 要： | 以Sobolev空间为工具,利用Galerkin法和局部延拓法,对源于FPU问题的一类具非线性本构关系的弹性梁方程弱解的存在唯一性问题进行了研究,得到以下结论:在一定的边界条件和初始条件下,证明了一类具非线性本构关系的弹性梁方程弱解的存在性;在此弹性梁方程弱解存在的条件下,证明了上述方程弱解的唯一性。
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| 关 键 词： | 非线性弹性梁方程 Galerkin法 弱解 存在唯一性 |
| 文章编号： | 1007-9432（2007）01-0091-04 |
| 收稿时间： | 2006-11-04 |
| 修稿时间： | 2006-11-04 |
The Existence and Uniqueness of Weak Solution for a Sort of Nonlinear Elastic Beam Equation |
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| YAN Si-qing,ZHANG Jian-wen.The Existence and Uniqueness of Weak Solution for a Sort of Nonlinear Elastic Beam Equation[J].Journal of Taiyuan University of Technology,2007,38(1):91-94. |
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| Authors: | YAN Si-qing ZHANG Jian-wen |
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| Institution: | College of Sciences of TUT , Taiyuan 030024 ,China |
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| Abstract: | We carry out some studies on existence and uniqueness of solutions of initial and boundary conditions of elastic beam equation with nonlinear constitutive relation,that source of FPU question,by means of the Galerkin method in the Sobolev space.Our main work includes the following.Under some certain initial and Boundary conditions.We verified with nonlinear constitutive relation elastic beam equation the existence uniqueness global weak solution on the initial conditions are shown.Moreover,the uniqueness of the story solution are proved. |
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| Keywords: | nonlinear elastic beam equations Galerkin method weak solution existence and uniqueness |
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