| 离散热传导方程稳态解的存在性 |
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| 引用本文： | 白亮,张广.离散热传导方程稳态解的存在性[J].青岛理工大学学报,2009,30(3):130-136. |
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| 作者姓名： | 白亮 张广 |
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| 作者单位： | 1. 青岛理工大学,理学院,青岛,266033
2. 天津商业大学,理学院,天津,300134 |
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| 摘 要： | 离散热传导方程的非退化稳态解的存在性对生产实践有着重要的意义,笔者构造了一个函数,使得带周期边界条件的一维离散热传导方程的解对应于此函数的临界点,然后通过使用Morse理论中的一些结果来讨论此函数的非退化临界点的存在性,从而得到了带周期边界条件的一维离散热传导方程至少存在两个非退化解的充分条件.最后通过一个例子说明所得的结论在具体的热传导方程中的应用.
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| 关 键 词： | 热传导方程 Morse理论 存在性 临界点 |
Existence of Steady-State Solutions for Discrete Heat Equation |
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| BAI Liang,ZHANG Guang.Existence of Steady-State Solutions for Discrete Heat Equation[J].Journal of Qingdao Technological University,2009,30(3):130-136. |
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| Authors: | BAI Liang ZHANG Guang |
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| Affiliation: | 1.School of Science;Qingdao Technological University;Qingdao 266033;China;2.School of Science;Tianjin Commerce University;Tianjin 300134;China |
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| Abstract: | Existence of nontrivial steady-state solutions for discrete heat equation is of great importance in practice.A function is constructed,which enables the steady-state solutions of discrete one-dimensional heat equation with periodic boundary value condition to correspond to its critical points.Existence of nontrivial critical points of the function is considered by using some results in Morse theory.In this way,sufficient conditions for the existence of nontrivial steady-state solutions for discrete one-dime... |
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| Keywords: | heat equation Morse theory existence critical point |
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