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 Izv. Vyssh. Uchebn. Zaved. Mat., 2011, Number 12, Pages 76–80 (Mi ivm8409)

Brief communications

Solvability of a multivalued filtering problem in a heterogeneous environment with a distributed source

S. S. Alekseyev, O. A. Zadvornov

Chair of Computational Mathematics, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: In this paper we formulate a generalized filtering problem in a heterogeneous environment in the presence of a source distributed along a line. Incompressible fluids obey a multivalued law with a linear growth at infinity. In this study we use the additive singularity extraction in the right hand side of the problem constraint. We represent the pressure field as the sum of a known solution to a certain linear problem and an unknown “additive term”. We reduce the problem under consideration to a variational inequality of the second kind in a Hilbert space (with respect to the mentioned “additive term”) and prove its solvability.

Keywords: nonlinear filtering of an incompressible fluid, heterogeneous environment, multivalued law, source distributed along a line, variational inequality.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:12, 63–66

Bibliographic databases:

UDC: 517.958+532.546
Presented by the member of Editorial Board: Ð. Ç. Äàóòîâ

Citation: S. S. Alekseyev, O. A. Zadvornov, “Solvability of a multivalued filtering problem in a heterogeneous environment with a distributed source”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 12, 76–80; Russian Math. (Iz. VUZ), 55:12 (2011), 63–66

Citation in format AMSBIB
\Bibitem{AleZad11} \by S.~S.~Alekseyev, O.~A.~Zadvornov \paper Solvability of a~multivalued filtering problem in a~heterogeneous environment with a~distributed source \jour Izv. Vyssh. Uchebn. Zaved. Mat. \yr 2011 \issue 12 \pages 76--80 \mathnet{http://mi.mathnet.ru/ivm8409} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2963467} \transl \jour Russian Math. (Iz. VUZ) \yr 2011 \vol 55 \issue 12 \pages 63--66 \crossref{https://doi.org/10.3103/S1066369X11120103} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84856282014}