Conservation laws and symmetries of radial generalized nonlinear p-Laplacian evolution equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:452

Article

Recio, Elena^1,2  Anco, Stephen C.¹ 

[1] Brock Univ, Dept Math & Stat, St Catharines, ON L2S 3A1, Canada

[2] Univ Cadiz, Fac Sci, Dept Math, Cadiz 11510, Spain

关键词: Nonlinear diffusion-reaction equation;    Conservation law;    Symmetry;    Group-invariant solution;    Gradient diffusivity;   

DOI  :  10.1016/j.jmaa.2017.03.050

来源: Elsevier

【 摘 要 】

A class of generalized nonlinear p-Laplacian evolution equations is studied. These equations model radial diffusion reaction processes in n >= 1 dimensions, where the diffusivity depends on the gradient of the flow. For this class, all local conservation laws of low-order and all Lie symmetries are derived. The physical meaning of the conservation laws is discussed, and one of the conservation laws is used to show that the nonlinear equation can be mapped invertibly into a linear equation by a hodograph transformation in certain cases. The symmetries are used to derive exact group-invariant solutions from solvable three-dimensional subgroups of the full symmetry group, which yields a direct reduction of the nonlinear equation to a quadrature. The physical and analytical properties of these exact solutions are explored, some of which describe moving interfaces and Green's functions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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