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Open AccessArticle

Projector Approach to Constructing Asymptotic Solution of Initial Value Problems for Singularly Perturbed Systems in Critical Case

by Galina Kurina 1,2,3,†
1
Voronezh State University, Voronezh 394018, Russia
2
Voronezh Institute of Law and Economics, Voronezh 394042, Russia
3
Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Moscow 119333, Russia
Voronezh State University, Universitetskaya pl.,1, Voronezh 394018, Russia.
Axioms 2019, 8(2), 56; https://doi.org/10.3390/axioms8020056
Received: 13 February 2019 / Revised: 20 April 2019 / Accepted: 21 April 2019 / Published: 8 May 2019
Under some conditions, an asymptotic solution containing boundary functions was constructed in a paper by Vasil’eva and Butuzov (Differ. Uravn. 1970, 6(4), 650–664 (in Russian); English transl.: Differential Equations 1971, 6, 499–510) for an initial value problem for weakly non-linear differential equations with a small parameter standing before the derivative, in the case of a singular matrix A ( t ) standing in front of the unknown function. In the present paper, the orthogonal projectors onto k e r A ( t ) and k e r A ( t ) (the prime denotes the transposition) are used for asymptotics construction. This approach essentially simplifies understanding of the algorithm of asymptotics construction. View Full-Text
Keywords: singular perturbations; initial value problems; asymptotics; critical case; projector approach singular perturbations; initial value problems; asymptotics; critical case; projector approach
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Kurina, G. Projector Approach to Constructing Asymptotic Solution of Initial Value Problems for Singularly Perturbed Systems in Critical Case. Axioms 2019, 8, 56.

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