Conditional Lie–Bäcklund Symmetries and Functionally Generalized Separation of Variables to Quasi-Linear Diffusion Equations with Source
Department of Information and Computational Science, He’nan Agricultural University, Zhengzhou 450002, China
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Symmetry 2020, 12(5), 844; https://doi.org/10.3390/sym12050844
Received: 19 January 2020 / Revised: 2 May 2020 / Accepted: 6 May 2020 / Published: 21 May 2020
(This article belongs to the Special Issue Conservation Laws and Symmetries of Differential Equations)
The conditional Lie–Bäcklund symmetry method is applied to investigate the functionally generalized separation of variables for quasi-linear diffusion equations with a source. The equations and the admitted conditional Lie–Bäcklund symmetries related to invariant subspaces are identified. The exact solutions possessing the form of the functionally generalized separation of variables are constructed for the resulting equations due to the corresponding symmetry reductions.
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Keywords:
conditional Lie–Bäcklund symmetry; separation of variables; invariant subspace; symmetry reduction; diffusion equation
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MDPI and ACS Style
Wang, R.; Ji, L. Conditional Lie–Bäcklund Symmetries and Functionally Generalized Separation of Variables to Quasi-Linear Diffusion Equations with Source. Symmetry 2020, 12, 844.
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