搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

扰动扩散方程初值问题的近似对称约化

李吉娜 朱晓宁 程利芳

引用本文:
Citation:

扰动扩散方程初值问题的近似对称约化

李吉娜, 朱晓宁, 程利芳

Approximate symmetry reduction for initial-value problem of perturbed diffusion equations

Li Ji-Na, Zhu Xiao-Ning, Cheng Li-Fang
PDF
导出引用
  • 本文利用近似广义条件对称方法研究一类带有源项的非线性扩散方程的初值问题. 给出所研究方程的分类并将偏微分方程的初值问题约化为常微分方程的初值问题, 通过求解约化后的常微分方程组可得相对应偏微分方程初值问题的近似解.
    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.
    • 基金项目: 国家自然科学基金(批准号: 11101332)和河南省自然科学基金(批准号: 102300410275, 122300410166)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11101332), and the Natural Science Foundation of Henan Province, China (Grant Nos. 102300410275, 122300410166).
    [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]
计量
  • 文章访问数:  5154
  • PDF下载量:  482
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-06-10
  • 修回日期:  2012-08-23
  • 刊出日期:  2013-01-05

/

返回文章
返回