A symmetry analysis of some classes of evolutionary nonlinear (2+1)-diffusion equations with variable diffusivity

Ashfaque H. Bokhari; Ahmad Y. Al Dweik; A. H. Kara; F. D. Zaman

doi:10.1007/s11071-010-9704-8

A symmetry analysis of some classes of evolutionary nonlinear (2+1)-diffusion equations with variable diffusivity

Ashfaque H. Bokhari
, Ahmad Y. Al Dweik
, A. H. Kara^*
, F. D. Zaman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper the (2+1)-nonlinear diffusion equation ut -div(f (u)gradu) = 0 with variable diffusivity is considered. Using the Lie method, a complete symmetry classification of the equation is presented. Reductions, via two-dimensional Lie subalgebras of the equation, to first- or second-order ordinary differential equations are given. In a few interesting cases exact solutions are presented.

Original language	English
Pages (from-to)	127-138
Number of pages	12
Journal	Nonlinear Dynamics
Volume	62
Issue number	1-2
DOIs	https://doi.org/10.1007/s11071-010-9704-8
State	Published - Oct 2010

Keywords

Complete classification
Variable diffusivity

ASJC Scopus subject areas

Control and Systems Engineering
Aerospace Engineering
Ocean Engineering
Mechanical Engineering
Applied Mathematics
Electrical and Electronic Engineering

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10.1007/s11071-010-9704-8

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title = "A symmetry analysis of some classes of evolutionary nonlinear (2+1)-diffusion equations with variable diffusivity",

abstract = "In this paper the (2+1)-nonlinear diffusion equation ut -div(f (u)gradu) = 0 with variable diffusivity is considered. Using the Lie method, a complete symmetry classification of the equation is presented. Reductions, via two-dimensional Lie subalgebras of the equation, to first- or second-order ordinary differential equations are given. In a few interesting cases exact solutions are presented.",

keywords = "Complete classification, Variable diffusivity",

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AU - Bokhari, Ashfaque H.

AU - Al Dweik, Ahmad Y.

AU - Kara, A. H.

AU - Zaman, F. D.

PY - 2010/10

Y1 - 2010/10

N2 - In this paper the (2+1)-nonlinear diffusion equation ut -div(f (u)gradu) = 0 with variable diffusivity is considered. Using the Lie method, a complete symmetry classification of the equation is presented. Reductions, via two-dimensional Lie subalgebras of the equation, to first- or second-order ordinary differential equations are given. In a few interesting cases exact solutions are presented.

AB - In this paper the (2+1)-nonlinear diffusion equation ut -div(f (u)gradu) = 0 with variable diffusivity is considered. Using the Lie method, a complete symmetry classification of the equation is presented. Reductions, via two-dimensional Lie subalgebras of the equation, to first- or second-order ordinary differential equations are given. In a few interesting cases exact solutions are presented.

KW - Complete classification

KW - Variable diffusivity

UR - https://www.scopus.com/pages/publications/84898544639

U2 - 10.1007/s11071-010-9704-8

DO - 10.1007/s11071-010-9704-8

M3 - Article

AN - SCOPUS:84898544639

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IS - 1-2

ER -

A symmetry analysis of some classes of evolutionary nonlinear (2+1)-diffusion equations with variable diffusivity

Abstract

Keywords

ASJC Scopus subject areas

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