| 微分方程解的相似结构初探与展望 |
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| 引用本文： | 李顺初. 微分方程解的相似结构初探与展望[J]. 西华大学学报(自然科学版), 2010, 29(2): 223-226,238 |
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| 作者姓名： | 李顺初 |
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| 作者单位： | 西华大学应用数学研究所,四川,成都,610039 |
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| 基金项目： | 国家"九五"重点攻关项目 |
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| 摘 要： | 针对二阶齐次线性常微分方程(组)的边值问题和二阶齐次线性偏微分方程(组)的混合问题,综述了分别对其解和Laplace空间解的相似结构理论的初步探讨的一些成果;分析了解的相似思想的形成及相关研究的意义,剖析了解的相似结构与定解方程和边值条件间的联系,发现了一种利用相似结构式和相似核函数构造定解问题的解的方法,介绍了它在解决渗流力学问题中的现有应用成果;最后,对微分方程解的相似结构理论的研究与应用前景进行了展望。
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| 关 键 词： | 微分方程 渗流力学 边值问题 相似结构 Laplace空间解 |
Preliminary Exploration and Prospects of the Similar Structure of Solutions of Differential Equations |
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| LI Shun-chu. Preliminary Exploration and Prospects of the Similar Structure of Solutions of Differential Equations[J]. Journal of Xihua University(Natural Science Edition), 2010, 29(2): 223-226,238 |
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| Authors: | LI Shun-chu |
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| Affiliation: | LI Shun-chu(Institute of Applied Mathematics,Xihua University,Chengdu 610039 China) |
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| Abstract: | Aiming at the boundary-value problem for second-order homogeneous linear ordinary differential equations(systems) and the mixed problem for second-order homogeneous linear partial differential equations(systems),this paper reviews some results of preliminary explorations with regard to the similar structure theory of their solutions or their Laplace space solutions;analyzes the formation idea of the similar solution and its significance of research;takes apart the relation between the similar structure of i... |
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| Keywords: | differential equation permeation fluid mechanics boundary-values problems similar structure solution of Laplace space |
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