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Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2011, Volume 153, Book 1, Pages 168–179 (Mi uzku913)  

Existence of solutions of filtration problems with multi-valued law in nonhomogeneous media in the presence of a point source

S. S. Alekseev, O. A. Zadvornov

Kazan (Volga Region) Federal University, Faculty of Computer Science and Cybernetics

Abstract: We formulate a generalized problem of filtration of incompressible fluid governed by a multi-valued law with a linear growth at infinity in nonhomogeneous media in the presence of a point source. We used an additive selection of a feature associated with the singularity of the right side. The solution is represented in the form of the sum of the known solution of a certain linear problem with a point source in the right side, and the unknown term. As for the unknown term, the problem is reduced to the solution of mixed variational inequality in Hilbert space. The existence theorem is proved.

Keywords: nonlinear filtration, multi-valued law, nonhomogeneous media, point source, variational inequality.

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UDC: 517.957
Received: 20.12.2010

Citation: S. S. Alekseev, O. A. Zadvornov, “Existence of solutions of filtration problems with multi-valued law in nonhomogeneous media in the presence of a point source”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 153, no. 1, Kazan University, Kazan, 2011, 168–179

Citation in format AMSBIB
\Bibitem{AleZad11}
\by S.~S.~Alekseev, O.~A.~Zadvornov
\paper Existence of solutions of filtration problems with multi-valued law in nonhomogeneous media in the presence of a~point source
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2011
\vol 153
\issue 1
\pages 168--179
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku913}


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