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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2017, Volume 10, Issue 2, Pages 63–73 (Mi vyuru372)  

This article is cited in 3 scientific papers (total in 3 papers)

Mathematical Modelling

Solution of irregular systems of partial differential equations using skeleton decomposition of linear operators

D. N. Sidorovab, N. A. Sidorovc

a Melentiev Energy Systems Institute SB RAS, Irkutsk, Russian Federation
b Irkutsk National Technical University, Irkutsk, Russian Federation
c Irkutsk State University, Irkutsk, Russian Federation

Abstract: The linear system of partial differential equations is considered. It is assumed that there is an irreversible linear operator in the main part of the system. The operator is assumed to enjoy the skeletal decomposition. The differential operators of such system are assumed to have sufficiently smooth coefficients. In the concrete situations the domains of such differential operators are linear manifolds of smooth enough functions with values in Banach space. Such functions are assumed to satisfy 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 a 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 certain initial and boundary conditions. The proposed approach can be generalized and applied to the boundary value problems in the nonlinear case. Presented results develop the theory of degenerate differential equations summarized in the monographs MR 87a:58036, Zbl 1027.47001.

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

Funding Agency Grant Number
International Science and Technology Cooperation Program 2015DFA70850
National Natural Science Foundation of China 61673398
Russian Science Foundation 14-19-00054
This work is fuilfilled within International Science and Technology Cooperation Program (No. 2015DFA70850) of China & Russia; NSFC Grant No. 61673398. The first author's work is partly supported by RSF Grant No. 14-19-00054.


DOI: https://doi.org/10.14529/mmp170205

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UDC: 517.9
MSC: 35G15, 35R25
Received: 28.12.2016
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Citation: D. N. Sidorov, N. A. Sidorov, “Solution of irregular systems of partial differential equations using skeleton decomposition of linear operators”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:2 (2017), 63–73

Citation in format AMSBIB
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\by D.~N.~Sidorov, N.~A.~Sidorov
\paper Solution of irregular systems of partial differential equations using skeleton decomposition of linear operators
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2017
\vol 10
\issue 2
\pages 63--73
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\crossref{https://doi.org/10.14529/mmp170205}
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\elib{http://elibrary.ru/item.asp?id=29274780}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. A. Sidorov, D. N. Sidorov, “Skeletnye razlozheniya lineinykh operatorov v teorii neregulyarnykh sistem s chastnymi proizvodnymi”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 20 (2017), 75–95  mathnet  crossref
    2. N. A. Sidorov, D. N. Sidorov, Yu. Li, “Oblasti prityazheniya tochek ravnovesiya nelineinykh sistem: ustoichivost, vetvlenie i razrushenie reshenii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 23 (2018), 46–63  mathnet  crossref
    3. N. A. Sidorov, “Classic solutions of boundary value problems for partial differential equations with operator of finite index in the main part of equation”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 27 (2019), 55–70  mathnet  crossref
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