具有幂率衰减边界层的奇摄动问题
Singularly Perturbed Problems with a Power-Law Attenuation Boundary Layer
DOI: 10.12677/AAM.2018.71013, PDF, HTML, XML, 下载: 1,353  浏览: 3,307 
作者: 孙玉娇：安徽工业大学，数理科学与工程学院，安徽 马鞍山
关键词: 奇摄动；三重根；幂率衰减边界层；渐近解；Singular Perturbation； Triple Root； Power-Law Boundary Layer； Asymptotic Solution
摘要: 本文主要研究退化方程具有三重根的二阶奇摄动方程边值问题。运用边界层函数法构造出解的形式渐近展开式，得到以幂率形式衰减的边界层函数。最后用上下解方法得到形式解存在性和一致有效估计。
Abstract: Singularly Perturbed Problems with a Power-Law Layer is studied in this paper. The method of boundary layer function is used to construct the formal asymptotic expansion of the solution, and get the attenuated boundary layer functions of power-law. The existence and uniformly valid ap-proximation of solutions are obtained by upper and lower solutions method.
文章引用：孙玉娇. 具有幂率衰减边界层的奇摄动问题[J]. 应用数学进展, 2018, 7(1): 104-108. https://doi.org/10.12677/AAM.2018.71013

参考文献

[1] Butuzov, V.F., Nefedov, N.N., Recke, L. and Schneider, K.R. (2013) On a Singularly Perturbed Initial Value Problem in the Case of a Double Root of the Degenerate Equation. Nonlinear Analysis, 83, 1-11.
https://doi.org/10.1016/j.na.2013.01.013
[2] 倪明康, 丁海云. 具有代数衰减的边界层问题[J]. 数学杂志, 2001, 31(3): 488-494.
[3] Zhu, H.-P. (1997) The Dirichlet Problem for Singularly Perturbed Quasilinear Second Order Differential System. Journal of Mathematical Analysis and Applications, 210, 308-336.
https://doi.org/10.1006/jmaa.1997.5405
[4] Vasil’eva, A.B. (2009) Two-Point Boundary Value Problem for a Singularly Perturbed Equation with a Reduced Equation Having Multiple Roots. Computational Mathematics and Mathematical Physics, 49, 1021-1032.
[5] Vasil’eva, A.B. (2011) Boundary Layers in the Solution of Singularly Perturbed Boundary Value Problem with a Degenerate Equation Having Roots of Multiplicity Two. Computational Mathematics and Mathematical Physics, 51, 351-354.
[6] Vasil’eva, A.B. and Nefedov, N.N. (1990) Asymptotic Methods in the Theory of Singular Perturbation. Vysshaya Shkola, Moscow. (In Russian)
[7] 倪明康, 林武忠. 微分不等式理论[M]. 北京: 科学出版社, 2012.

为你推荐