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Matematicheskie Trudy, 2006, Volume 9, Number 2, Pages 191–204 (Mi mt53)  
A Method for Constructing Solutions to Linear Systems of Partial Differential Equations

A. A. Shlapunov

Krasnoyarsk State University
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Abstract: We obtain some conditions of solvability in Sobolev spaces for the systems of linear partial differential equations and deduce the corresponding formulas for solutions to these systems. The solutions are given as the sum of the series whose terms are the iterations of some pseudodifferential operators constructed explicitly.
Key words: overdetermined systems of partial differential equations, operator equations of the first kind.
Received: 21.10.2005
English version:
Siberian Advances in Mathematics, 2007, Volume 17, Issue 2, Pages 144–152
DOI: https://doi.org/10.3103/S1055134407020046
Bibliographic databases:
UDC: 517.95+517.98
Language: Russian
Citation: A. A. Shlapunov, “A Method for Constructing Solutions to Linear Systems of Partial Differential Equations”, Mat. Tr., 9:2 (2006), 191–204; Siberian Adv. Math., 17:2 (2007), 144–152
Citation in format AMSBIB
\Bibitem{Shl06}
\by A.~A.~Shlapunov
\paper A Method for Constructing Solutions to Linear Systems of Partial Differential Equations
\jour Mat. Tr.
\yr 2006
\vol 9
\issue 2
\pages 191--204
\mathnet{http://mi.mathnet.ru/mt53}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2301605}
\elib{https://elibrary.ru/item.asp?id=9530052}
\transl
\jour Siberian Adv. Math.
\yr 2007
\vol 17
\issue 2
\pages 144--152
\crossref{https://doi.org/10.3103/S1055134407020046}
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