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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.
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    [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))
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    [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))
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    [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.
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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

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