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

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

¹安庆师范学院桐城教学部, 安徽桐城 231402;²蚌埠学院数学与物理系, 安徽蚌埠 233030;³南京信息工程大学数学与统计学院, 南京 210044;⁴安徽师范大学数学系, 安徽芜湖 241000

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
计量
- 文章访问数: 1150
- HTML全文浏览量: 129
- PDF下载量: 940
- 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

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

¹Tongcheng Teaching Department, Anqing Normal University, Tongcheng, Anhui 231402, P.R.China;²Department of Mathematics and Physics, Bengbu University, Bengbu, Anhui 233030, P.R.China;³College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, P.R.China;⁴Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241000, P.R.China

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

摘要

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.
- 非线性 /
- 两参数 /
- 反应扩散
Abstract: The model for a class of highorder nonlinear reaction diffusion singularly perturbed problems with double parameters was addressed. With the singular perturbation method, the structure of the solution to the problem was discussed in the cases of double related small parameters. Firstly, the outer solution to the boundary value problem was given. Secondly, the variable of multiple scales was introduced to obtain the boundary layer correction term for the solution. Then the stretched variable was applied to the boundary neighborhood to get the initial layer correction term. Finally, the theorem of differential inequalities was constructed and the uniformly valid asymptotic expansion of the solution to the problem was proved. The proposed method possesses the advantages of convenient use and high accuracy.
- nonlinear /
- double parameters /
- reaction diffusion

HTML全文

参考文献(24)

[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.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 1150
HTML全文浏览量: 129
PDF下载量: 940
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

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

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）.

计量

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

计量

目录

留言板

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

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）.

计量

出版历程

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

计量

出版历程

目录

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）.