双参数非线性非局部奇摄动抛物型初始-边值问题的广义解

冯依虎; 莫嘉琪

doi:10.21656/1000-0887.380008

双参数非线性非局部奇摄动抛物型初始-边值问题的广义解

doi: 10.21656/1000-0887.380008

冯依虎¹,
莫嘉琪²

¹亳州学院电子与信息工程系, 安徽亳州 236800;²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(11202106)；安徽省教育厅自然科学基金(KJ2015A347；KJ2017A702)；安徽省高校优秀青年人才支持计划重点项目(gxyqZD2016520)

详细信息

作者简介:
冯依虎（1982—），男，副教授，硕士(E-mail: fengyihubzsz@163.com)；莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

中图分类号: O175.29
计量
- 文章访问数: 1094
- HTML全文浏览量: 150
- PDF下载量: 457
- 被引次数: 0
出版历程
- 收稿日期: 2017-01-19
- 修回日期: 2017-03-15
- 刊出日期: 2017-12-15

Generalized Solutions to Nonlinear Nonlocal Singularly Perturbed Parabolic Initial-Boundary Problems With Two Parameters

FENG Yi-hu¹,
MO Jia-qi²

¹Department of Electronics and Information Engineering, Bozhou College, Bozhou, Anhui 236800, P.R.China;²School of Mathematics & Computer Science, Anhui Normal University, Wuhu, Anhui 241003, P.R.China

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

摘要

摘要: 研究了一类广义抛物型方程奇摄动问题.首先在一定的条件下, 提出了一类具有两参数的非线性非局部广义抛物型方程初始边值问题.其次证明了相应问题解的存在性.然后, 通过Fredholm积分方程得到了初始边值问题的外部解.再利用泛函分析理论和伸长变量及多重尺度法, 分别构造了初始边值问题广义解的边界层、初始层项，从而得到了问题的形式渐近展开式.最后利用不动点理论证明了对应的非线性非局部广义抛物型方程的奇异摄动初始边值问题的广义解的渐近展开式的一致有效性.
- 奇异摄动 /
- 渐近展开 /
- 一致有效性
Abstract: A class of generalized parabolic equation singular perturbation problems were considered. Firstly, under suitable conditions, a class of nonlinear nonlocal generalized parabolic equation initial-boundary value problems with two parameters were raised. Secondly, the existence of solutions to corresponding problems was proved. Next, from the Fredholm integral equation, the outer solutions to the initial-boundary value problems were found, and the boundary and initial layer terms were structured by means of the theory of functional analysis, the stretched variables and the multiscale methods, respectively. Then the formal asymptotic expansion of the problem was obtained. Finally, according to the fixed point theorem, the uniform validity of the asymptotic expansion of generalized solutions to the corresponding nonlinear nonlocal initial-boundary value problems was proved.
- singular perturbation /
- asymptotic expansion /
- uniform validity

HTML全文

参考文献(13)

[1]	Bartu L, Morosanu G. Singularly Perturbed Boundary-Value Problems[M]. Basel: Birkhauserm Verlag AG, 2007.
[2]	de Jager E M, JIANG Fu-ru. The Theory of Singular Perturbation [M]. Amsterdam: North-Holland Publishing Co, 1996.
[3]	Kellogg R B, Kopteva N. A singularly perturbed semi-linear reaction-diffusion problem in a polygonal domain[J].Journal of Differential Equations,2010,248 (1): 184-208.
[4]	TIAN Can-rong, ZHU Peng. Existence and asymptotic behavior of solutions for quasilinear parabolic systems[J].Acta Applicandae Mathematicae,2012,121(1): 157-173.
[5]	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.
[6]	Skrynnikov Y. Solving initial value problem by matching asymptotic expansions[J]. SIAM Journal on Applied Mathematics, 2012,72(1): 405-416.
[7]	Martinez S, Wolanski N. A singular perturbation problem for a quasi-linear operator satisfying the natural condition of Lieberman[J].SIAM J Math Anal,2009,41(1): 318-359.
[8]	MO Jia-qi. Singular perturbation for a class of nonlinear reaction diffusion systems[J]. Science in China(Ser A),1989,32(11): 1306-1315.
[9]	MO Jia-qi. Approximate solution of homotopic mapping to solitary wave for generalized nonlinear KdV system[J]. Chin Phys Lett, 2009,26(1): 010204.
[10]	MO Jia-qi, LIN Wan-tao. Generalized variation iteration solution of an atmosphere-ocean oscillator model for global climate[J]. Journal of Systems Science & Complexity, 2011,24(2): 271-276.
[11]	冯依虎, 石兰芳, 汪维刚, 等. 一类广义非线性强阻尼扰动发展方程的行波解[J]. 应用数学和力学, 2015,36(3): 315-324.(FENG Yi-hu, SHI Lan-fang, WANG Wei-gang, et al. The traveling wave solution for a class of generalized nonlinear strong damping disturbed evolution equations[J]. Applied Mathematics and Mechanics,2015,36(3): 315-324.(in Chinese))
[12]	冯依虎, 石兰芳, 许永红, 等. 一类大气尘埃等离子体扩散模型研究[J]. 应用数学和力学, 2015,36(6): 639-650.(FENG Yi-hu, SHI Lan-fang, XU Yong-hong, et al. The study for a class of atomy plasma diffusion model in atmosphere[J]. Applied Mathematics and Mechanics,2015,36(6): 639-650.(in Chinese))
[13]	史娟荣, 朱敏, 莫嘉琪. 广义Schrdinger扰动耦合系统孤子解 [J]. 应用数学和力学, 2016,37(3): 319-330.(SHI Juan-rong, ZHU Min, MO Jia-qi. Solitary solutions to generalized Schrdinger disturbed coupled systems[J]. Applied Mathematics and Mechanics,2016,37(3): 319-330.(in Chinese))

施引文献

资源附件(0)

访问统计

计量

文章访问数: 1094
HTML全文浏览量: 150
PDF下载量: 457
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

双参数非线性非局部奇摄动抛物型初始-边值问题的广义解

doi: 10.21656/1000-0887.380008

作者简介:
冯依虎（1982—），男，副教授，硕士(E-mail: fengyihubzsz@163.com)；莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

计量

Generalized Solutions to Nonlinear Nonlocal Singularly Perturbed Parabolic Initial-Boundary Problems With Two Parameters

计量

目录

留言板

双参数非线性非局部奇摄动抛物型初始-边值问题的广义解

doi: 10.21656/1000-0887.380008

作者简介: 冯依虎（1982—），男，副教授，硕士(E-mail: fengyihubzsz@163.com)；莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

计量

出版历程

Generalized Solutions to Nonlinear Nonlocal Singularly Perturbed Parabolic Initial-Boundary Problems With Two Parameters

计量

出版历程

目录

作者简介:
冯依虎（1982—），男，副教授，硕士(E-mail: fengyihubzsz@163.com)；莫嘉琪(1937—),男,教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).