具有不连续源项的二阶半线性系统边值问题的奇摄动
Singular Perturbation for Boundary Value Problem of a Second-Order Semi-Linear System with Discontinuous Source Terms
摘要: 本文讨论了一类带有不连续源项的二阶半线性系统边值问题。首先，用边界函数法和缝接法构造出原问题的形式渐近解；然后运用上下解定理证明形式解的一致有效性。最后给出一个例子验证了结果的有效性。
Abstract: In this paper, a singularly perturbed boundary value problem of second-order semi-linear system with discontinuous source terms is discussed. Firstly, we use the boundary function method and sewing method to construct formal asymptotic solution to the original problem. Then, the uniformly validity of the solution obtained is proved by the lower and upper solutions theorem. Finally, an example is given as an illustration.
文章引用：李静, 谢峰. 具有不连续源项的二阶半线性系统边值问题的奇摄动[J]. 应用数学进展, 2019, 8(8): 1341-1351. https://doi.org/10.12677/AAM.2019.88158

参考文献

[1] 刘树德, 鲁世平, 姚静荪, 陈怀军. 奇异摄动边界层和内部理论[M]. 北京: 科学出版社, 2012.
[2] 周明儒, 杜增吉, 王广瓦. 奇异摄动中的微分不等式理论[M]. 北京: 科学出版社, 2012.
[3] 倪明康, 林武忠. 奇异摄动问题中的渐近理论[M]. 北京: 高等教育出版社, 2009.
[4] 张伟江, 周明儒, 林武忠, 倪明康, 刘树德, 谢峰, 仇璘. 奇异摄动导论[M]. 北京: 科学出版社, 2014.
[5] Aguilar, G. and Lisbona, F. (1997) Singular Perturbation on a Subdomain. Journal of Mathematical Analysis and Applications, 210, 292-307. [Google Scholar] [CrossRef] 
[6] De Falco, C. and O’Riordan, E. (2010) Interior Layers in a Reac-tion-Diffusion Equation with a Discontinuous Diffusion Coefficient. International Journal of Numerical Analysis and Modeling, 7, 444-461.
[7] Chern, I. and Shu, Y. (2007) A Coupling Interface Method for Elliptic Interface Problems. Journal of Computational Physics, 225, 2138-2174. [Google Scholar] [CrossRef] 
[8] Ding, H., Ni, M., Lin, W. and Cao, Y. (2012) Singularly Perturbed Semi-Linear Boundary Value Problem with Discontinuous Func-tion. Acta Mathematica Scientia, 32, 793-799. [Google Scholar] [CrossRef] 
[9] 包立平. 一类具有不连续源的奇摄动半线性微分方程组边值问题[J]. 高校应用数学学报, 2017, 32(4): 413-422.
[10] Rao, S.C.S. and Chawla, S. (2019) Parameter-Uniform Convergence of a Numerical Method for a Coupled System of Sin-gularly Perturbed Semilinear Reaction-Diffusion Equations with Boundary and Interior Layers. Journal of Computational and Applied Mathematics, 352, 223-239. [Google Scholar] [CrossRef] 
[11] 林红绪, 杨李凡, 胡雨欣. 一类带不连续源项的二阶半线性奇摄动Robin边值问题[J]. 应用数学, 2015, 28(1): 47-56.

为你推荐