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.
"Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator." Abstr. Appl. Anal. 2012 (SI18) 1 - 16, 2012. https://doi.org/10.1155/2012/120192