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Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie, 2014, Volume 7, Issue 3, Pages 5–22
DOI: https://doi.org/10.14529/mmp140301
(Mi vyuru140)
 

This article is cited in 12 scientific papers (total in 12 papers)

Review Articles

A multipoint initial-final value problem for a linear model of plane-parallel thermal convection in viscoelastic incompressible fluid

S. A. Zagrebina

South Ural State University, Chelyabinsk, Russian Federation
References:
Abstract: The linear model of plane-parallel thermal convection in a viscoelastic incompressible Kelvin–Voigt material amounts to a hybrid of the Oskolkov equations and the heat equations in the Oberbeck–Boussinesq approximation on a two-dimensional region with Bénard's conditions. We study the solvability of this model with the so-called multipoint initial-final conditions. We use these conditions to reconstruct the parameters of the processes in question from the results of multiple observations at various points and times. This enables us, for instance, to predict emergency situations, including the violation of continuity of thermal convection processes as a result of breaching technology, and so forth.
For thermal convection models, the solvability of Cauchy problems and initial-final value problems has been studied previously. In addition, the stability of solutions to the Cauchy problem has been discussed. We study a multipoint initial-final value problem for this model for the first time. In addition, in this article we prove a generalized decomposition theorem in the case of a relatively sectorial operator. The main result is a theorem on the unique solvability of the multipoint initial-final value problem for the linear model of plane-parallel thermal convection in a viscoelastic incompressible fluid.
Keywords: multipoint initial-final value problem; Sobolev-type equation; generalized splitting theorem; linear model of plane-parallel thermal convection in viscoelastic incompressible fluid.
Received: 14.05.2014
Document Type: Article
MSC: 35K70, 60H30
Language: English
Citation: S. A. Zagrebina, “A multipoint initial-final value problem for a linear model of plane-parallel thermal convection in viscoelastic incompressible fluid”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 7:3 (2014), 5–22
Citation in format AMSBIB
\Bibitem{Zag14}
\by S.~A.~Zagrebina
\paper A multipoint initial-final value problem for a linear model of plane-parallel thermal convection in viscoelastic incompressible fluid
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2014
\vol 7
\issue 3
\pages 5--22
\mathnet{http://mi.mathnet.ru/vyuru140}
\crossref{https://doi.org/10.14529/mmp140301}
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  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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