Geodesic
Solvability of a~multivalued filtering problem in a~heterogeneous environment with a~distributed source
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2011), pp. 76-80

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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. 
@article{IVM_2011_12_a9,
     author = {S. S. Alekseyev and O. A. Zadvornov},
     title = {Solvability of a~multivalued filtering problem in a~heterogeneous environment with a~distributed source},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--80},
     publisher = {mathdoc},
     number = {12},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_12_a9/}
}
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S. S. Alekseyev; O. A. Zadvornov. Solvability of a~multivalued filtering problem in a~heterogeneous environment with a~distributed source. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2011), pp. 76-80. http://geodesic.mathdoc.fr/item/IVM_2011_12_a9/