Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration

doi:10.1088/1674-1056/19/1/010301

中国物理B ›› 2010, Vol. 19 ›› Issue (1): 10301-010301.doi: 10.1088/1674-1056/19/1/010301

Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration

赵丽¹, 傅景礼¹, 陈本永²

(1)Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; (2)Institute of Mechanical and Automation Control Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China

收稿日期:2009-05-29 修回日期:2009-08-10 出版日期:2010-01-15 发布日期:2010-01-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10672143 and 60575055).

Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration

Zhao Li(赵丽)^a), Fu Jing-Li(傅景礼)^a)†, and Chen Ben-Yong(陈本永)^b)

^a Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; ^b Institute of Mechanical and Automation Control Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received:2009-05-29 Revised:2009-08-10 Online:2010-01-15 Published:2010-01-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10672143 and 60575055).

摘要/Abstract

摘要： The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation of concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentration under the infinitesimal transformation with respect to the generalized coordinates and time, the determining equations of Lie symmetries are presented. The Lie groups of transformation and infinitesimal generators of this equation are obtained. The conserved quantities associated with the nonlinear diffusion equation of concentration are derived by integrating the characteristic equations. Also, the solutions of the two-dimensional nonlinear diffusion equation of concentration can be obtained.

Abstract: The Lie symmetries and conserved quantities of a two-dimensional nonlinear diffusion equation of concentration are considered. Based on the invariance of the two-dimensional nonlinear diffusion equation of concentration under the infinitesimal transformation with respect to the generalized coordinates and time, the determining equations of Lie symmetries are presented. The Lie groups of transformation and infinitesimal generators of this equation are obtained. The conserved quantities associated with the nonlinear diffusion equation of concentration are derived by integrating the characteristic equations. Also, the solutions of the two-dimensional nonlinear diffusion equation of concentration can be obtained.

Key words: Lie symmetry, conserved quantity, nonlinear, diffusion equation of concentration

中图分类号: (Transport processes)

05.60.-k

02.20.Qs (General properties, structure, and representation of Lie groups) 02.30.Jr (Partial differential equations)

赵丽, 傅景礼, 陈本永. Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration[J]. 中国物理B, 2010, 19(1): 10301-010301.

Zhao Li(赵丽), Fu Jing-Li(傅景礼), and Chen Ben-Yong(陈本永). Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration[J]. Chin. Phys. B, 2010, 19(1): 10301-010301.

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Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration

Lie symmetries and conserved quantities for a two-dimensional nonlinear diffusion equation of concentration

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