| 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]. 数学年刊A辑(中文版), 2015, 36(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-DimensionalInvariant Subspaces of Generalized InhomogeneousNonlinear Diffusion Equations |
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| ZHU Chunrong and DOU Cailing. Equivalent Transformations and Higher-DimensionalInvariant Subspaces of Generalized InhomogeneousNonlinear Diffusion Equations[J]. Chinese Annals of Mathematics, 2015, 36(3): 291-302 |
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| Authors: | ZHU Chunrong and DOU Cailing |
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| Affiliation: | Corresponding author. College of Mathematics and Computer Science, AnhuiNormal 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 equationsare given by the pressure transformations and equivalent transformations related to theinvariant subspace method. Higher-dimensional invariant subspaces of equivalent equationsare obtained. From this, the generalized separable variables solutions of the generalizedinhomogeneous nonlinear diffusion equations are constructed. Some examples are presentedto illustrate the procedure. |
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| Keywords: | Nonlinear diffusion equations Invariant subspace method Equivalenttransformations Pressure transformations |
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