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Recent Progress in Study of Singular Perturbation Problems (莫嘉琪)
时间:2010/3/12   文章来源:   [打印] [收藏] [关闭]
     

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MO Jia-qi (莫嘉琪)1,3, NI Ming-kang(倪明康)2,3
1. Department of Mathematics, Anhui Normal University, Wuhu 241000, Anhui, P. R. China
2. Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China
3. Division of Computational Science, E-Institutes of Shanghai Universities, Shanghai Jiaotong University,
Shanghai 200240, P. R. China
Abstract :Some results for the singular perturbation theory, methods and applications in the new century are reviewed in this paper. It could be found that in the recent decade, many approximate methods have been developed and refined, including the method of averaging, boundary layer methods, methods of matched asymptotic expansion and methods of multiple scales. An overview is given on the new work about various problems, such as the reaction diffusion, turning points, boundary layers, shock waves, stability problem, solitons, attractors, canard solution, scattering light wave and neuron network, etc. And then, a great number of applied problems are solved in applied mathematics, computational mathematics, fluid mechanics, elastic mechanics, optics, thermophysics, quantum mechanics, plasm physics, physical chemistry, analytical chemistry, epidemiology, neurology, engineering science, environment science, bionomics, atmosphere physics, ocean climate, aeronautics and astrnatics and so on, from which only some examples are extracted and described in this review.
Keywords :singular perturbation, differential equations, boundary value problem

Project supported by the National Natural Science Foundation of China (Grant No.40676016), the State Key Development
Program for Basic Research of China (Grant Nos.2003CB415101-03, 2004CB418304), the Key Project of the Chinese Academy
of Sciences (Grant No.KZCX3-SW-221), and the E-Insitutes of Shanghai Municipal Education Commission (Grant No.E03004)
Corresponding author MO Jia-qi, Prof., E-mail: mojiaqi@mail.ahnu.edu.cn

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