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The approximate functional variable separation for the porous medium equation with perturbed nonlinear source is studied. Complete classification of the perturbed equation which admits approximate functional separable solutions is obtained. The main solving procedure for the approximate functional variable separation approach is shown by way of examples, and the corresponding approximate functional separable solutions to the resulting equations are then constructed.
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Keywords:
- porous medium equation /
- approximate generalized conditional symmetry /
- approximate functional variable separation approach
[1] Olver P J 1993 Applications of Lie Groups to Differential Equations (New York: Springer) p75
[2] Qian X M, Lou S Y 1996 Acta Phys. Sin. 45 721 (in Chinese) [钱贤民, 楼森岳 1996 45 721]
[3] Gu S L, Zhang H B 2006 Acta Phys. Sin. 55 5594 (in Chinese) [顾书龙, 张宏斌 2006 55 5594]
[4] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese) [贾利群, 崔金超, 张耀宇, 罗绍凯 2009 58 16]
[5] Kalnins E G, Miller W 1985 J. Math. Phys. 26 2168
[6] Dolye P W, Vassiliou P J 1998 Int. J. Nonlinear Mech. 33 315
[7] Cao C W 1990 Sci. China A 33 528
[8] Lou S Y 2000 Phys. Lett. A 277 94
[9] Qu C Z, Zhang S L, Liu R C 2000 Physica D 144 97
[10] Zhang S L, Lou S Y, Qu C Z 2003 J. Phys. A 36 12223
[11] Zhang J F, Xu C Z, He B G 2004 Acta Phys. Sin. 53 3652 (in Chinese) [张解放, 徐昌智, 何宝钢 2004 53 3652]
[12] Shen S F 2006 Acta Phys. Sin. 55 1011 (in Chinese) [沈守枫 2006 55 1011]
[13] Baikov V A, Gazizov R K, Ibragimov N H 1989 Math. USSR Sb. 64 427
[14] Fushchich W I, Shtelen W M 1989 J. Phys. A 22 L887
[15] Mahomed F M, Qu C Z 2000 J. Phys. A 33 343
[16] Kara A H, Mahomed F M, Qu C Z 2000 J. Phys. A 33 6601
[17] Zhang S L, Qu C Z 2006 Chin. Phys. Lett. 23 527
[18] Mo J Q, Lin W T, Lin Y H 2007 Acta Phys. Sin. 56 3127 (in Chinese) [莫嘉琪, 林万涛, 林一骅 2007 56 3127]
[19] Li J N, Zhang S L 2011 Chin. Phys. Lett. 28 030201
[20] Shi L F, Zhou X C 2010 Acta Phys. Sin. 59 2915 (in Chinese) [石兰芳, 周先春 2010 59 2915]
[21] Zhou X C, Lin W T, Lin Y H, Mo J Q 2010 Acta Phys. Sin. 59 2173 (in Chinese) [周先春, 林万涛, 林一骅, 莫嘉琪 2010 59 2173]
[22] Ye W C, Li B, Wang J 2011 Acta Phys. Sin. 60 030207 (in Chinese) [叶望川, 李彪, 王佳 2011 60 030207]
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[1] Olver P J 1993 Applications of Lie Groups to Differential Equations (New York: Springer) p75
[2] Qian X M, Lou S Y 1996 Acta Phys. Sin. 45 721 (in Chinese) [钱贤民, 楼森岳 1996 45 721]
[3] Gu S L, Zhang H B 2006 Acta Phys. Sin. 55 5594 (in Chinese) [顾书龙, 张宏斌 2006 55 5594]
[4] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese) [贾利群, 崔金超, 张耀宇, 罗绍凯 2009 58 16]
[5] Kalnins E G, Miller W 1985 J. Math. Phys. 26 2168
[6] Dolye P W, Vassiliou P J 1998 Int. J. Nonlinear Mech. 33 315
[7] Cao C W 1990 Sci. China A 33 528
[8] Lou S Y 2000 Phys. Lett. A 277 94
[9] Qu C Z, Zhang S L, Liu R C 2000 Physica D 144 97
[10] Zhang S L, Lou S Y, Qu C Z 2003 J. Phys. A 36 12223
[11] Zhang J F, Xu C Z, He B G 2004 Acta Phys. Sin. 53 3652 (in Chinese) [张解放, 徐昌智, 何宝钢 2004 53 3652]
[12] Shen S F 2006 Acta Phys. Sin. 55 1011 (in Chinese) [沈守枫 2006 55 1011]
[13] Baikov V A, Gazizov R K, Ibragimov N H 1989 Math. USSR Sb. 64 427
[14] Fushchich W I, Shtelen W M 1989 J. Phys. A 22 L887
[15] Mahomed F M, Qu C Z 2000 J. Phys. A 33 343
[16] Kara A H, Mahomed F M, Qu C Z 2000 J. Phys. A 33 6601
[17] Zhang S L, Qu C Z 2006 Chin. Phys. Lett. 23 527
[18] Mo J Q, Lin W T, Lin Y H 2007 Acta Phys. Sin. 56 3127 (in Chinese) [莫嘉琪, 林万涛, 林一骅 2007 56 3127]
[19] Li J N, Zhang S L 2011 Chin. Phys. Lett. 28 030201
[20] Shi L F, Zhou X C 2010 Acta Phys. Sin. 59 2915 (in Chinese) [石兰芳, 周先春 2010 59 2915]
[21] Zhou X C, Lin W T, Lin Y H, Mo J Q 2010 Acta Phys. Sin. 59 2173 (in Chinese) [周先春, 林万涛, 林一骅, 莫嘉琪 2010 59 2173]
[22] Ye W C, Li B, Wang J 2011 Acta Phys. Sin. 60 030207 (in Chinese) [叶望川, 李彪, 王佳 2011 60 030207]
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