| 一般非齐次非线性扩散方程的等价变换和高维不变子空间 |
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| 引用本文： | 朱春蓉,窦彩玲.一般非齐次非线性扩散方程的等价变换和高维不变子空间[J].河海大学学报(自然科学版),2015(3):291-302. |
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| 作者姓名： | 朱春蓉 窦彩玲 |
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| 作者单位： | 通讯作者：安徽师范大学数学与计算机科学学院, 安徽 芜湖 241000,安徽师范大学数学与计算机科学学院, 安徽 芜湖 241000 |
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| 基金项目： | 本文受到国家自然科学基金 (No.11301007) 的资助. |
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| 摘 要： | 结合压力变换和不变子空间方法中的等价变换, 给出了一般非齐次非线性扩散方程的等价方程,
并给出了等价方程的高维不变子空间. 由此构造了一般非齐次非线性扩散方程的广义分离变量解,
并给出了几个例子解释这个过程.
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| 关 键 词： | 非线性扩散方程 不变子空间方法 等价变换 压力变换 |
Equivalent Transformations and Higher-Dimensional
Invariant Subspaces of Generalized Inhomogeneous
Nonlinear Diffusion Equations |
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| ZHU Chunrong and DOU Cailing.Equivalent Transformations and Higher-Dimensional
Invariant Subspaces of Generalized Inhomogeneous
Nonlinear Diffusion Equations[J].Journal of Hohai University (Natural Sciences ),2015(3):291-302. |
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| Authors: | ZHU Chunrong and DOU Cailing |
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| Institution: | Corresponding author. College of Mathematics and Computer Science, Anhui
Normal University, Wuhu 241000, Anhui, China. and College of Mathematics and Computer Science, Anhui Normal University,
Wuhu 241000, Anhui, China. |
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| Abstract: | Equations equivalent to the generalized inhomogeneous nonlinear diffusion equations
are given by the pressure transformations and equivalent transformations related to the
invariant subspace method. Higher-dimensional invariant subspaces of equivalent equations
are obtained. From this, the generalized separable variables solutions of the generalized
inhomogeneous nonlinear diffusion equations are constructed. Some examples are presented
to illustrate the procedure. |
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| Keywords: | Nonlinear diffusion equations Invariant subspace method Equivalent
transformations Pressure transformations |
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