Abstract:
A method is studied for constructing a regularized asymptotic expression for the solution of a Cauchy problem in the case of a multiple spectrum. The paper consists of two parts. The first part deals with the case when the operator is similar to a single Jordan cell, and the second with the case when the operator is similar to an operator with several Jordan cells. In both cases the structure matrix does not have degeneracies. The structure of a fundamental system of solutions is presented.
Bibliography: 13 titles.
Citation:
A. G. Eliseev, “Singular perturbation theory for systems of differential equations in the case of multiple spectrum of the limit operator. I, II”, Math. USSR-Izv., 25:2 (1985), 315–357
\Bibitem{Eli84}
\by A.~G.~Eliseev
\paper Singular perturbation theory for systems of differential equations in the case of multiple spectrum of the limit operator.~I,~II
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 2
\pages 315--357
\mathnet{http://mi.mathnet.ru/eng/im1505}
\crossref{https://doi.org/10.1070/IM1985v025n02ABEH001284}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=764307}
\zmath{https://zbmath.org/?q=an:0604.34033}
Linking options:
https://www.mathnet.ru/eng/im1505
https://doi.org/10.1070/IM1985v025n02ABEH001284
https://www.mathnet.ru/eng/im/v48/i5/p999
This publication is cited in the following 4 articles:
K. I. Chernyshov, “Cauchy operator of a non-stationary linear differential equation with a small parameter at the derivative”, Sb. Math., 196:8 (2005), 1165–1208
A. M. Dzhuraev, “Sovremennoe sostoyanie teorii singulyarnykh vozmuschenii”, Trudy Vserossiiskoi nauchnoi konferentsii (26–28 maya 2004 g.). Chast 3, Differentsialnye uravneniya i kraevye zadachi, Matem. modelirovanie i kraev. zadachi, SamGTU, Samara, 2004, 79–82
S. A. Lomov, A. G. Eliseev, “Asymptotic integration of singularly perturbed problems”, Russian Math. Surveys, 43:3 (1988), 1–63
A. G. Eliseev, “Singular perturbation theory for systems of differential equations in the case of multiple spectrum of the limit operator. III”, Math. USSR-Izv., 25:3 (1985), 475–500
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