Abstract and Applied Analysis
Volume 2012 (2012), Article ID 120192, 16 pages
http://dx.doi.org/10.1155/2012/120192
Research Article

Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator

Burkhan T. Kalimbetov, Marat A. Temirbekov, and Zhanibek O. Khabibullayev

Department of Mathematics, A. Yasawi International Kazakh-Turkish University, Turkestan 161200, Kazakhstan

Received 2 March 2012; Accepted 3 April 2012

Academic Editor: Allaberen Ashyralyev

Copyright © 2012 Burkhan T. Kalimbetov et al. 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.

Abstract

The regularization method is applied for the construction of algorithm for an asymptotical solution for linear singular perturbed systems with the irreversible limit operator. The main idea of this method is based on the analysis of dual singular points of investigated equations and passage in the space of the larger dimension, what reduces to study of systems of first-order partial differential equations with incomplete initial data.