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非线性扩散方程的广义分离变量解 被引量:1

Generalized separation of variables solutions to nonlinear diffusion equations
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摘要 目的构造非线性扩散方程的广义分离变量解。方法条件Lie-Bcklund对称方法。结果得到了非线性扩散方程的广义分离变量解。结论用条件Lie-Bcklund对称方法可以构造非线性扩散方程的广义分离变量解,这些解与不变子空间关系密切,有丰富的理论及实践意义。 Aim To construct generalized separation of variables solutions of nonlinear diffusion equations. Meth- ods Conditional Lie Baecklund symmetry method. Results Generalized separation of variables solutions to nonlin- ear diffusion equations are obtained. Conclusion The generalized separation of variables solutions to the nonliear diffusion equations can be constructed due to the conditional Lie Backlund symmetry method, which is of close relation to the invariant subspace, and has large numbers of theoric and practical applications.
作者 姬利娜 冯玮
出处 《西北大学学报(自然科学版)》 CAS CSCD 北大核心 2011年第4期587-588,592,共3页 Journal of Northwest University(Natural Science Edition)
基金 陕西省自然科学基础研究计划基金资助项目(2009JQ1003) 西北大学优秀博士论文基金资助项目(08YYB03) 河南省教育厅自然科学研究基金资助项目(2008A110008)
关键词 非线性扩散方程 广义分离变量解 条件Lie-Bcklund对称 不变子空间 nonliear diffusion equations generalized separation of variables solutions conditional Lie Backlundsymmetry invariant subspace method
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  • 1Qu Changzheng, Zhu Chunrong. Classification of cou- pled systems with two-component nonlinear diffusion equations by the invariant subspaee method[J]. Journal of Physics A: Mathematical and Theoretical, 2009, 42 (47) : 475201(1-27).
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  • 6姬利娜,冯玮.带有热源项的非线性扩散方程的精确解[J].纯粹数学与应用数学,2010,26(5):725-727. 被引量:2
  • 7MA Wen-Xiu.A refined invariant subspace method and applications to evolution equations[J].Science China Mathematics,2012,55(9):1769-1778. 被引量:21

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