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一类奇异摄动燃烧模型的渐近解

史娟荣 莫嘉琪

史娟荣, 莫嘉琪. 一类奇异摄动燃烧模型的渐近解[J]. 应用数学和力学, 2016, 37(7): 691-698. doi: 10.21656/1000-0887.360293
引用本文: 史娟荣, 莫嘉琪. 一类奇异摄动燃烧模型的渐近解[J]. 应用数学和力学, 2016, 37(7): 691-698. doi: 10.21656/1000-0887.360293
SHI Juan-rong, MO Jia-qi. Asymptotic Solutions to a Class of Singular Perturbation Burning Models[J]. Applied Mathematics and Mechanics, 2016, 37(7): 691-698. doi: 10.21656/1000-0887.360293
Citation: SHI Juan-rong, MO Jia-qi. Asymptotic Solutions to a Class of Singular Perturbation Burning Models[J]. Applied Mathematics and Mechanics, 2016, 37(7): 691-698. doi: 10.21656/1000-0887.360293

一类奇异摄动燃烧模型的渐近解

doi: 10.21656/1000-0887.360293
基金项目: 国家自然科学基金(41275062;11202106);安徽省高等学校省级自然科学研究项目(KJ2015A418);国家高级访问学者项目
详细信息
    作者简介:

    史娟荣(1981—),女,副教授,硕士(E-mail: ahjdshjr@126.com);莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

  • 中图分类号: O175.14

Asymptotic Solutions to a Class of Singular Perturbation Burning Models

Funds: The National Natural Science Foundation of China(41275062;11202106)
  • 摘要: 讨论了一类具有两参数的非线性奇异摄动的燃烧模型.首先,利用摄动方法, 得到了燃烧模型的外部解;其次,引入一个伸长变量, 构造了燃烧模型解的初始层的校正项; 然后, 利用多重尺度方法和合成展开方法构造了模型解的边界层校正项, 并由此得到了原初始边值问题的渐近解;最后,利用微分不等式相关的理论证明了所得到的渐近解的一致有效性.用该文的求解方法简单而可行.
  • [1] de Jager E M, JIANG Fu-ru. The Theory of Singular Perturbation[M]. Amsterdam: North-Holland Publishing Co, 1996.
    [2] Barbu L, Moroanu 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 Mathematical Science,Vol56. Springer-Verlag, 1984.
    [4] Martínez 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.
    [5] 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.
    [6] TIAN Can-rong, ZHU Peng. Existence and asymptotic behavior of solutions for quasilinear parabolic systems[J]. Acta Applicandae Mathematicae,2012,121(1): 157-173.
    [7] Skrynnikov Y. Solving initial value problem by matching asymptotic expansions[J]. SIAM Journal on Applied Mathematics,2012,72(1): 405-416.
    [8] 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.
    [9] MO Jia-qi. Singular perturbation for a class of nonlinear reaction diffusion systems[J]. Science in China(Ser A),1989,32(11): 1306-1315.
    [10] 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.
    [11] MO Jia-qi. Approximate solution of homotopic mapping to wave solitary for generalized nonlinear KdV system[J]. Chinese Physics Letters,2009,26(1): 010204-1-010204-4.
    [12] MO Jia-qi. Homotopic mapping solving method for gain fluency of a laser pulse amplifier[J]. Science in China (Series G): Physics, Mechanics & Astronomy,2009,39(7): 1007-1010.
    [13] MO Jia-qi, CHEN Xian-feng. Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation[J]. Chinese Physics B,2010,10(10): 100203-1-100203-4.
    [14] 莫嘉琪, 刘树德, 唐荣荣. 一类奇异摄动非线性方程Robin问题激波的位置[J]. 物理学报, 2010,59(7): 4403-4408.(MO Jia-qi, LIU Shu-de, TANG Rong-rong. Shock position for a class of Robin problems of singularly perturbed nonlinear equation[J]. Acta Physica Sinica,2010,59(7): 4403-4408.(in Chinese))
    [15] MO Jia-qi, CHEN Huai-jun. The corner layer solution of Robin problem for semilinear equation[J]. Mathematica Applicata,2012,25(1): 1-4.
    [16] MO Jia-qi, WANG Wei-gang, CHEN Xian-feng, SHI Lan-fang. The shock wave solutions for singularly perturbed time delay nonlinear boundary value problems with two papameters[J]. Mathematica Applicata,2014,27(3): 470-475.
    [17] 史娟荣, 石兰芳, 莫嘉琪. 一类非线性强阻尼扰动发展方程的解[J]. 应用数学和力学, 2014,35(9): 1046-1054.(SHI Juan-rong, SHI Lan-fang, MO Jia-qi. Solutions to a class of nonlinear strong-damp disturbed evolution equations[J]. Applied Mathematics and Mechanics,2014,35(9): 1046-1054.(in Chinese))
    [18] SHI Juan-rong, LIN Wan-tao, MO Jia-qi. The singularly perturbed solution for a class of quasilinear nonlocal problem for higher order with two parameters[J]. Acta Scientiarum Naturalium Universitatis Nankaiensis,2015,48(1): 85-91.
    [19] 史娟荣, 吴钦宽, 莫嘉琪. 非线性扰动广义NNV系统的孤立子渐近行波解[J]. 应用数学和力学, 2015,36(9): 1003-1010.(SHI Juan-rong, WU Qin-kuan, MO Jia-qi. Asymptotic travelling wave soliton solutions for nonlinear disturbed generalized NNV systems[J]. Applied Mathematics and Mechanics,2015,36(9): 1003-1010.(in Chinese))
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出版历程
  • 收稿日期:  2015-10-27
  • 修回日期:  2015-11-27
  • 刊出日期:  2016-07-15

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