First-Order Sign-Invariants and Exact Solutions of the Radially Symmetric Nonlinear Diffusion Equations with Gradient-Dependent Diffusivities

The sign-invariant theory is used to study the radially symmetric nonlinear diffusion equations with gradient-dependent diffusivities. The first-order non-stationary sign-invariants and the first-order non-autonomous sign-invariants admitted by the governing equations are identified. As a consequenc...

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Bibliographic Details
Published in:	Symmetry (Basel) Vol. 14; no. 2; p. 386
Main Authors:	Ji, Lina, Luo, Xiankang, Zeng, Jiao, Xiao, Min, Meng, Yuanhua
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01-02-2022
Subjects:	conditional Lie-Bäcklund symmetry exact solution Exact solutions Invariants Mathematical analysis nonlinear diffusion equation Partial differential equations sign-invariant Symmetry
Online Access:	Get full text
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Summary:	The sign-invariant theory is used to study the radially symmetric nonlinear diffusion equations with gradient-dependent diffusivities. The first-order non-stationary sign-invariants and the first-order non-autonomous sign-invariants admitted by the governing equations are identified. As a consequence, the exact solutions to the resulting equations are constructed due to the corresponding reductions. The phenomena of blow-up, extinction and behavior of some solutions are also described.
ISSN:	2073-8994 2073-8994
DOI:	10.3390/sym14020386