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 The Bulletin of Irkutsk State University. Series Mathematics, 2017, Volume 20, Pages 75–95 (Mi iigum306)

Skeleton decomposition of linear operators in the theory of nonregular systems of partial differential equations

N. A. Sidorova, D. N. Sidorovabc

a Irkutsk State University, 1, K. Marx st., Irkutsk, 664003
b Melentiev Energy Systems Institute SB RAS, 130, Lermontov st., Irkutsk, 664033
c Irkutsk National Research Technical University, 84, Lermontov st., Irkutsk, 664074

Abstract: The linear system of partial differential equations is considered. It is assumed that there is the irreversible linear operator in the main part of the system, which enjoy the skeletal decomposition. The differential operators is such system are assumed to have a sufficiently smooth coefficients. In the concrete situations the domains of such differential operators are linear manifolds of smooth enough functions with ranges in Banach space. Such functions are assumed to satisfy an additional boundary conditions. The concept of a skeleton chain of linear operator is introduced. It is assumed that the operator generates a skeleton chain of the finite length. In this case, the problem of solution of given system is reduced to a regular split system of equations. The system is resolved with respect to the highest differential expressions taking into account the certain initial and boundary conditions. The possible generalization of the approach and the application to the formulation of boundary value problems in the nonlinear case. Presented results develop the theory of degenerate differential equations in the monographs N. A. Sidorov [General regularization questions in problems of branching theory. (1982; MR 87a:58036)]; N. A. Sidorov, B. V. Loginov, A. V. Sinitsyn and M. V. Falaleev [Lyapunov–Schmidt methods in nonlinear analysis and applications (Math. Appl. 550, Kluwer Acad. Publ., Dordrecht) (2002; Zbl 1027.47001)].

Keywords: ill-posed problems, Cauchy problems, irreversible operator, skeleton decomposition, skeleton chain, boundary value problems.

 Funding Agency Grant Number Ïðîãðàììà ìåæäóíàðîäíîãî íàó÷íî-òåõíè÷åñêîãî ñîòðóäíè÷åñòâà Êèòàÿ è Ðîññèè 2015DFA70850 National Natural Science Foundation of China 61673398

DOI: https://doi.org/10.26516/1997-7670.2017.20.75

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Bibliographic databases:

UDC: 517.518.15
MSC: 35R25, 47A50, 47N20

Citation: N. A. Sidorov, D. N. Sidorov, “Skeleton decomposition of linear operators in the theory of nonregular systems of partial differential equations”, The Bulletin of Irkutsk State University. Series Mathematics, 20 (2017), 75–95

Citation in format AMSBIB
\Bibitem{SidSid17} \by N.~A.~Sidorov, D.~N.~Sidorov \paper Skeleton decomposition of linear operators in the theory of nonregular systems of partial differential equations \jour The Bulletin of Irkutsk State University. Series Mathematics \yr 2017 \vol 20 \pages 75--95 \mathnet{http://mi.mathnet.ru/iigum306} \crossref{https://doi.org/10.26516/1997-7670.2017.20.75}