一类奇异摄动燃烧模型的渐近解

史娟荣; 莫嘉琪

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

史娟荣^1,2,
莫嘉琪³

¹安徽机电职业技术学院, 安徽芜湖 241002;²上海交通大学数学系, 上海 200240;³安徽师范大学数学计算机科学学院, 安徽芜湖 241003

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
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- 被引次数: 0
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

Asymptotic Solutions to a Class of Singular Perturbation Burning Models

SHI Juan-rong^1,2,
MO Jia-qi³

¹Anhui Technical College of Mechanical and Electrical Engineering, Wuhu, Anhui 241002, P.R.China;²Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P.R.China;³School of Mathematics & Computer Science, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

Funds: The National Natural Science Foundation of China(41275062;11202106)

摘要

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.
- 燃烧模型 /
- 渐近解 /
- 奇异摄动
Abstract: A class of nonlinear singularly perturbed burning models with two parameters were discussed. Firstly, the outer solution to the burning model was constructed with the perturbation method. Secondly, through the introduction of a stretched variable, the initial layer correction term of the solution to the burning model was constructed. Then the multi-scale method and the composite expansion method were used to build the boundary layer correction term of the model solution and find the asymptotic solution to the original initial boundary value problem. Finally, the uniform validity of the obtained asymptotic solution was proved according to the theory of differential inequalities. The proposed solving method for this class of nonlinear singularly perturbed burning models is convenient and practicable.
- burning model /
- asymptotic solution /
- singular perturbation

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参考文献(19)

[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))