ASYMPTOTIC SOLUTIONS TO INITIAL VALUE PROBLEMS FOR SINGULARLY PERTURBED QUASI-LINEAR IMPULSIVE SYSTEMS

This paper investigates a singularly perturbed quasi-linear impulsive differential system with singularities present both in the differential equations and in the impulse functions. The boundary function method is employed to derive the main results. A uniform asymptotic approximation with higher ac...

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Published inVestnik KazNU. Serii͡a︡ matematika, mekhanika, informatika Vol. 127; no. 3
Main Authors Aviltay, Nauryzbay, Uaissov, Alpamys
Format Journal Article
LanguageEnglish
Published 30.09.2025
Online AccessGet full text
ISSN1563-0277
2617-4871
2617-4871
DOI10.26577/JMMCS202512734

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Abstract This paper investigates a singularly perturbed quasi-linear impulsive differential system with singularities present both in the differential equations and in the impulse functions. The boundary function method is employed to derive the main results. A uniform asymptotic approximation with higher accuracy is constructed and a complete asymptotic expansion is obtained. Theoretical findings are supported by illustrative examples and numerical simulations. The analysis reveals the presence of boundary and interior layers caused by the singular perturbation and impulsive effects. Sufficient conditions for the existence and uniqueness of the solution are established. The results contribute to the theoretical understanding of impulsive systems with complex singular structures and may be applicable to various problems in applied mathematics. 
AbstractList This paper investigates a singularly perturbed quasi-linear impulsive differential system with singularities present both in the differential equations and in the impulse functions. The boundary function method is employed to derive the main results. A uniform asymptotic approximation with higher accuracy is constructed and a complete asymptotic expansion is obtained. Theoretical findings are supported by illustrative examples and numerical simulations. The analysis reveals the presence of boundary and interior layers caused by the singular perturbation and impulsive effects. Sufficient conditions for the existence and uniqueness of the solution are established. The results contribute to the theoretical understanding of impulsive systems with complex singular structures and may be applicable to various problems in applied mathematics. 
Author Uaissov, Alpamys
Aviltay, Nauryzbay
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