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

一类双参数非线性高阶反应扩散方程的摄动解法

汪维刚 许永红 石兰芳 莫嘉琪

汪维刚, 许永红, 石兰芳, 莫嘉琪. 一类双参数非线性高阶反应扩散方程的摄动解法[J]. 应用数学和力学, 2014, 35(12): 1383-1391. doi: 10.3879/j.issn.1000-0887.2014.12.010
引用本文: 汪维刚, 许永红, 石兰芳, 莫嘉琪. 一类双参数非线性高阶反应扩散方程的摄动解法[J]. 应用数学和力学, 2014, 35(12): 1383-1391. doi: 10.3879/j.issn.1000-0887.2014.12.010
WANG Wei-gang, XU Yong-hong, SHI Lan-fang, MO Jia-qi. Perturbation Method for a Class of High-Order Nonlinear Reaction Diffusion Equations With Double Parameters[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1383-1391. doi: 10.3879/j.issn.1000-0887.2014.12.010
Citation: WANG Wei-gang, XU Yong-hong, SHI Lan-fang, MO Jia-qi. Perturbation Method for a Class of High-Order Nonlinear Reaction Diffusion Equations With Double Parameters[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1383-1391. doi: 10.3879/j.issn.1000-0887.2014.12.010

一类双参数非线性高阶反应扩散方程的摄动解法

doi: 10.3879/j.issn.1000-0887.2014.12.010
基金项目: 国家自然科学基金(11202106);安徽省高等学校省级自然科学研究项目(KJ2013A133;KJ2014A151);江苏省自然科学基金(13KJB170016)
详细信息
    作者简介:

    汪维刚(1969—),男,安徽桐城人,副教授,硕士(E-mail: wwg12345@126.com);莫嘉琪(1937—),男,浙江德清人,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

  • 中图分类号: O175.29

Perturbation Method for a Class of High-Order Nonlinear Reaction Diffusion Equations With Double Parameters

Funds: The National Natural Science Foundation of China(11202106)
  • 摘要: 研究了一类两参数非线性反应扩散奇摄动问题的模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的情形下作了讨论.首先,构造问题的外部解; 之后在区域的边界邻域构造局部坐标系,再在该邻域中引入多尺度变量,得到问题解的边界层校正项; 然后引入伸长变量,构造初始层校正项,并得到问题解的形式渐近展开式;最后建立了微分不等式理论,并由此证明了问题的解的一致有效的渐近展开式.用上述方法得到的各次近似解,具有便于求解、精度高等特点.
  • [1] de Jager E M, JIANG Fu-ru. The Theory of Singular Perturbation[M]. Amsterdam: North-Holland Publishing Co, 1996.
    [2] 〖JP2〗Barbu L, Morosanu G. Singularly Perturbed Boundary-Value Problems[M]. Basel: Birkhauserm Verlag AG, 2007.
    [3] Chang K W, Howes F A. Nonlinear Singular Perturbation Phenomena: Theory and Applications[M]. Applied Mathemaical Science,56. New York: Springer-Verlag, 1984.
    [4] Pao C V. Nonlinear Parabolic Elliptic Equations [M]. New York: Plenum Press, 1992.
    [5] Martinez S, Wolanski N. A singular perturbation problem for a quasi-linear operator satisfying the natural growth condition of Lieberman[J]. SIAM Journal on Mathematical Analysis,2009,41(1): 318-359.
    [6] Kellogg R B, Kopteva N. A singularly perturbed semilinear reaction-diffusion problem in a polygonal domain[J]. Journal of Differential Equations,2010,248(1): 184-208.
    [7] TIAN Can-rong, ZHU Peng. Existence and asymptotic behavior of solutions for quasilinear parabolic systems[J]. Acta Applicandae Mathematicae,2012,121(1): 157-173.
    [8] Skrynnikov Y. Solving initial value problem by matching asymptotic expansions[J]. SIAM Journal on Applied Mathematics,2012,72(1): 405-416.
    [9] Samusenko P F. Asymptotic integration of degenerate singularly perturbed systems of parabolic partial differential equations[J]. Journal of Mathematical Sciences,2013,189(5): 834-847.
    [10] 汪维刚, 林万涛, 石兰芳, 莫嘉琪. 非线性扰动时滞长波系统孤波近似解[J]. 物理学报, 2014,63(11): 110204.(WANG Wei-gang, LIN Wan-tao, SHI Lan-fang, MO Jia-qi. Approximate solution of solitary wave for nonlinear-disturbed time delay long-wave system[J]. Acta Physica Sinica,2014,63(11): 110204.(in Chinese))
    [11] WANG Wei-gang, SHI Lan-fang, XU Yong-hong, MO Jia-qi. Generalized solution of the singularly perturbed boundary value problems for semilinear elliptic equation of higher order with two parameters[J]. 南开大学学报(自然科学版), 2014,47(2): 47-81.
    [12] WANG Wei-gang, SHI Juan-rong, SHI Lan-fang, MO Jia-qi. The singularly perturbed solution of nonlinear nonlocal equation for higher order[J]. 南开大学学报(自然科学版), 2014,47(1): 13-18.
    [13] 许永红, 林万涛, 徐惠, 姚静荪, 莫嘉琪. 一类相对论转动动力学模型[J]. 兰州大学学报(自然科学版), 2012,48(1): 100-103.(XU Yong-hong, LIN Wan-tao, XU Hui, YAO Jing-sun, MO Jia-qi. A class of rotational relativistic rotation dynamic model[J]. Journal Lanzhou University(Natural Sciences),2012,48(1): 100-103.(in Chinese))
    [14] SHI Lan-fang, CHEN Cai-sheng, ZHOU Xian-chun. The extended auxiliary equation method for the KdV equation with variable coefficients[J]. Chinese Physics B,2011,20(10):100507.
    [15] 石兰芳, 林万涛, 温朝晖, 莫嘉琪. 一类奇摄动Robin问题的内部冲击波解[J]. 应用数学学报, 2013,36(1): 108-114.(SHI Lan-fang, LIN Wan-tao, WEN Zhao-hui, MO Jia-qi. Internal shock solution for a class of singularly perturbed Robin problems[J]. Acta Mathematicae Applicatae Sinica,2013,36(1): 108-114.(in Chinese))
    [16] MO Jia-qi, LIN Wan-tao. A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation[J]. Acta Mathematicae Applicatae Sinica,2006,22(1): 27-32.
    [17] MO Jia-qi. A class of singularly perturbed differential-difference reaction diffusion equation[J]. Advance in Mathematics,2009,38(2): 227-231.
    [18] MO Jia-qi, LIN Wan-tao. Asymptotic solution of activator inhibitor systems for nonlinear reaction diffusion equations[J]. Journal of Systems Science and Complexity,2008,20(1): 119-128.
    [19] MO Jia-qi. Homotopic mapping solving method for gain fluency of a laser pulse amplifier[J]. Science in China Ser G,2009,52(7): 1007-1010.
    [20] MO Jia-qi, CHEN Xian-feng. Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation[J]. Chinese Physics B,2010,19(10): 100203.
    [21] MO Jia-qi. Approximate solution of homotopic mapping to solitary wave for generalized nonlinear KdV system[J].Chinese Physics Letters,2009,26(1): 010204.
    [22] MO Jia-qi, LIN Wan-tao, WANG Hui. Variational iteration solving method of a sea-air oscillator model for the ENSO[J]. Progress in Natural Science,2007,17(2): 230-232.
    [23] MO Jia-qi, LIN Wan-tao. Generalized variation iteration solution of an atmosphere-ocean oscillator model for global climate[J]. Journal of Systems Science and Complexity, 2011,24 (2): 271-276.
    [24] MO Jia-qi. Singularly perturbed reaction diffusion problem for nonlinear boundary condition with two parameters[J]. Chinese Physics B,2010,19(1): 010203.
  • 加载中
计量
  • 文章访问数:  635
  • HTML全文浏览量:  13
  • PDF下载量:  933
  • 被引次数: 0
出版历程
  • 收稿日期:  2014-08-01
  • 修回日期:  2014-10-24
  • 刊出日期:  2014-12-15

目录

    /

    返回文章
    返回