Solvability of a multivalued filtering problem in a heterogeneous environment with a distributed source |
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Authors: | S S Alekseev O A Zadvornov |
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Institution: | 1.Kazan (Volga Region) Federal University,Kazan,Russia |
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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. |
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