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In this paper, the approximate symmetry reduction for the initial-value problem of perturbed diffusion equations with source term is studied by the approximate generalized conditional symmetry. The classification of governing equations is given, and the Cauchy problem of partial differential equations is reduced to initial-value problem of ordinary differential equations. Finally, the approximate solution is obtained by solving the reduced system of equations.
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Keywords:
- perturbed diffusion equation /
- initial-value problem /
- approximate generalized conditional symmetry
[1] Qu C Z 1999 Commun. Theor. Phys. 31 581
[2] [3] Yung C M, Verburg K, Baveye P 1994 Int. J. Nonlinear Mech. 29 273
[4] [5] Nayfeh A H 2000 Perturbation Methods (New York: John Wiley)
[6] Olver P J 1993 Applications of Lie Group to Differential Equations (2nd ed)(New York: Springer)
[7] [8] Ovsiannikov L V 1982 The Group Analysis of Differential Equations (New York: Academic Press)
[9] [10] [11] Bluman G W, Anco S C 2002 Symmetry and Integration Methods for Differential Equations (New York: Springer)
[12] [13] Baikov V A, Gazizov R K, Ibragimov N H 1988 Mat. Sb. 136 435
[14] Fushchich W I, Shtelen W M 1989 J. Phys. A: Math. Gen. 22 L887
[15] [16] [17] Mahomed F M, Qu C Z 2000 J. Phys. A: Math. Gen., 33 343
[18] Kara A H, Mahomed F M, Qu C Z 2000 J. Phys. A: Math. Gen. 33 6601
[19] [20] Zhang S L, Wang Y, Lou S Y 2007 Commun. Theor. Phys. 47 975
[21] [22] Burde G I 2001 Phys A: Math．Gen. 34 5535
[23] [24] Jiao X Y, Yao R X, Lou S Y 2009 Chin. Phys. Lett. 26 040202
[25] [26] [27] Jiao X Y 2011 Acta Phys. Sin. 12 120201 (in Chinese) [焦小玉 2011 物理学报 12 120201]
[28] [29] Moran M J, Gaggioli R A 1969 J. Eng. Math. 3 151
[30] Zhdanov R Z 1995 J. Phys. A: Math. Gen. 28 3841
[31] [32] [33] Basarab-Horwath P, Zhdanov R Z 2001 J. Math. Phys. 42 376
[34] Hydon P E 2005 J. Math. Anal. Appl. 309 103
[35] [36] [37] Zhang Z Y, Chen Y F 2010 Physics Letters A 374 1117
[38] [39] Cherniha R, Kovalenko S 2009 J. Phys. A: Math. Theor. 42 355202
[40] Li J N, Zhang S L 2011 Chin. Phys. Lett. 28 030201
[41] [42] Li J N, Zhang S L, Su J R 2010 Commun. Theor. Phys. 53 28
[43] -
[1] Qu C Z 1999 Commun. Theor. Phys. 31 581
[2] [3] Yung C M, Verburg K, Baveye P 1994 Int. J. Nonlinear Mech. 29 273
[4] [5] Nayfeh A H 2000 Perturbation Methods (New York: John Wiley)
[6] Olver P J 1993 Applications of Lie Group to Differential Equations (2nd ed)(New York: Springer)
[7] [8] Ovsiannikov L V 1982 The Group Analysis of Differential Equations (New York: Academic Press)
[9] [10] [11] Bluman G W, Anco S C 2002 Symmetry and Integration Methods for Differential Equations (New York: Springer)
[12] [13] Baikov V A, Gazizov R K, Ibragimov N H 1988 Mat. Sb. 136 435
[14] Fushchich W I, Shtelen W M 1989 J. Phys. A: Math. Gen. 22 L887
[15] [16] [17] Mahomed F M, Qu C Z 2000 J. Phys. A: Math. Gen., 33 343
[18] Kara A H, Mahomed F M, Qu C Z 2000 J. Phys. A: Math. Gen. 33 6601
[19] [20] Zhang S L, Wang Y, Lou S Y 2007 Commun. Theor. Phys. 47 975
[21] [22] Burde G I 2001 Phys A: Math．Gen. 34 5535
[23] [24] Jiao X Y, Yao R X, Lou S Y 2009 Chin. Phys. Lett. 26 040202
[25] [26] [27] Jiao X Y 2011 Acta Phys. Sin. 12 120201 (in Chinese) [焦小玉 2011 物理学报 12 120201]
[28] [29] Moran M J, Gaggioli R A 1969 J. Eng. Math. 3 151
[30] Zhdanov R Z 1995 J. Phys. A: Math. Gen. 28 3841
[31] [32] [33] Basarab-Horwath P, Zhdanov R Z 2001 J. Math. Phys. 42 376
[34] Hydon P E 2005 J. Math. Anal. Appl. 309 103
[35] [36] [37] Zhang Z Y, Chen Y F 2010 Physics Letters A 374 1117
[38] [39] Cherniha R, Kovalenko S 2009 J. Phys. A: Math. Theor. 42 355202
[40] Li J N, Zhang S L 2011 Chin. Phys. Lett. 28 030201
[41] [42] Li J N, Zhang S L, Su J R 2010 Commun. Theor. Phys. 53 28
[43]
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