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Báo cáo hóa học: " Research Article On Step-Like Contrast Structure of Singularly Perturbed Systems"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On Step-Like Contrast Structure of Singularly Perturbed Systems | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 634324 17 pages doi 10.1155 2009 634324 Research Article On Step-Like Contrast Structure of Singularly Perturbed Systems Mingkang Ni and Zhiming Wang Department of Mathematics East China Normal University Shanghai 200241 China Correspondence should be addressed to Zhiming Wang zmwang@math.ecnu.edu.cn Received 15 April 2009 Revised 5 July 2009 Accepted 14 July 2009 Recommended by Donal O Regan The existence of a step-like contrast structure for a class of high-dimensional singularly perturbed system is shown by a smooth connection method based on the existence of a first integral for an associated system. In the framework of this paper we not only give the conditions under which there exists an internal transition layer but also determine where an internal transition time is. Meanwhile the uniformly valid asymptotic expansion of a solution with a step-like contrast structure is presented. Copyright 2009 M. Ni and Z. Wang. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction The problem of contrast structures is a singularly perturbed problem whose solutions with both internal transition layers and boundary layers. In recent years the study of contrast structures is one of the hot research topics in the study of singular perturbation theory. In western society most works on internal layer solutions concentrate on singularly perturbed parabolic systems by geometric method see 1 and the references therein . In Russia the works on singularly perturbed ordinary equations are concerned by boundary function method 2-5 . One of the basic difficulties for such a problem is unknown of where an internal transition layer is in advance. Butuzov and Vasil eva initiated the concept of contrast structures in 1987 6 and studied the .