Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

doi:10.1088/1674-1056/22/10/100202

中国物理B ›› 2013, Vol. 22 ›› Issue (10): 100202-100202.doi: 10.1088/1674-1056/22/10/100202

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

吉飞宇, 杨春晓

College of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China

收稿日期:2013-03-24 修回日期:2013-04-11 出版日期:2013-08-30 发布日期:2013-08-30
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10671156) and the Natural Science Foundation of Shaanxi Province of China (Grant No. SJ08A05).

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

Ji Fei-Yu (吉飞宇), Yang Chun-Xiao (杨春晓)

College of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China

Received:2013-03-24 Revised:2013-04-11 Online:2013-08-30 Published:2013-08-30
Contact: Ji Fei-Yu E-mail:feiyuji@xauat.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10671156) and the Natural Science Foundation of Shaanxi Province of China (Grant No. SJ08A05).

摘要/Abstract

摘要： By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source u_t=(A(u)u_x)_x+∈B(u,u_x). A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approximate solutions to the resulting perturbed equations are constructed via examples.

关键词: quasi-linear diffusion equation, approximate derivative-dependent functional separable solution, approximate generalized conditional symmetry

Abstract: By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source u_t=(A(u)u_x)_x+∈B(u,u_x). A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approximate solutions to the resulting perturbed equations are constructed via examples.

Key words: quasi-linear diffusion equation, approximate derivative-dependent functional separable solution, approximate generalized conditional symmetry

中图分类号: (Partial differential equations)

02.30.Jr

02.20.Sv (Lie algebras of Lie groups)

吉飞宇, 杨春晓. Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source[J]. 中国物理B, 2013, 22(10): 100202-100202.

Ji Fei-Yu (吉飞宇), Yang Chun-Xiao (杨春晓). Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source[J]. Chin. Phys. B, 2013, 22(10): 100202-100202.

参考文献 32

[1]	Olver P J 1993 Applications of Lie Groups to Differential Equations (New York: Springer)
[2]	Bluman G W and Anco S C 2004 Symmetry and Integration Methods for Differential Equations (New York: Springer-Verlag)
[3]	Ma S H, Fang J P, Ren Q B and Yang Z 2012 Chin. Phys. B 21 050511
[4]	Ma S H and Fang J P 2009 Z. Naturforsch. 64a 37
[5]	Wang X X, Han Y L, Zhang M L and Jia L Q 2013 Chin. Phys. B 22 020201
[6]	Zhao G L, Chen L Q, Fu J L and Hong F Y 2013 Chin. Phys. B 22 030205
[7]	Bluman G W and Cole J D 1969 J. Math. Mech. 18 1025
[8]	Qu C Z 1997 Stud. Appl. Math. 99 107
[9]	Bluman G W, Reid J D and Kumei S 1988 J. Math. Phys. 29 806
[10]	Qu C Z 2007 J. Phys. A: Math. Theor. 40 1757
[11]	Miller W 1977 Symmetry and Separation of Variables (Massachusetts: Addison-Wesley, Reading)
[12]	Kalnins E G and Miller W 1985 J. Math. Phys. 26 1560
[13]	Dolye P W and Vassiliou P J 1998 Int. J. Nonlinear Mech. 33 315
[14]	Zhdanov R Z 1997 J. Math. Phys. 38 1197
[15]	Cao C W 1990 Sci. China A: Phys. Mech. Astron. 33 528
[16]	Lou S Y and Chen L L 1999 J. Math. Phys. 40 6491
[17]	Qu C Z, Zhang S L and Liu R C 2000 Physica D 144 97
[18]	Zhang S L, Lou S Y and Qu C Z 2003 J. Phys. A: Math. Gen. 36 12223
[19]	Zhang S L, Lou S Y and Qu C Z 2006 Chin. Phys. 15 2765
[20]	Kevorkian J and Cole J D 1980 Perturbation Methods in Applied Mathematics (New York: Springer-Verlag)
[21]	Baikov V A, Gazizov R K and Ibragimov N H 1991 J. Math. Sci. 55 1450
[22]	Mahomed F M and Qu C Z 2000 J. Phys. A: Math. Gen. 33 343
[23]	Kara A H, Mahomed F M and Qu C Z 2000 J. Phys. A: Math. Gen. 33 6601
[24]	Zhang S L and Qu C Z 2006 Chin. Phys. Lett. 23 527
[25]	Jiao X Y, Gao Y and Lou S Y 2009 Sci. China G: Phys. Mech. Astron. 52 1169
[26]	Lin W T, Zhang Y and Mo J Q 2013 Chin. Phys. B 22 030205
[27]	Lin W T, Lin Y H and Mo J Q 2012 Chin. Phys. B 21 010204
[28]	Wu J L and Lou S Y 2012 Chin. Phys. B 21 120204
[29]	Hassanabadi H, Yazarloo B H and Lu L L 2012 Chin. Phys. Lett. 29 020303
[30]	Li J N and Zhang S L 2011 Chin. Phys. Lett. 28 030201
[31]	Ji F Y and Zhang S L 2012 Acta Phys. Sin. 61 080202 (in Chinese)
[32]	Zhang S L, Ji F Y and Qu C Z 2012 Commun. Theor. Phys. 58 175

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 32

相关文章 1

Metrics

本文评价

推荐阅读 0