| 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,2015,36(3):291~302 |
| 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 |
| Equivalent Transformations and Higher-DimensionalInvariant Subspaces of Generalized InhomogeneousNonlinear Diffusion Equations |
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| DOI： |
| 中文关键词: 非线性扩散方程, 不变子空间方法, 等价变换, 压力变换 |
| 英文关键词:Nonlinear diffusion equations, Invariant subspace method, Equivalent
transformations, Pressure transformations |
| 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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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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