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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2014, Volume 7, Issue 3, Pages 5–22 (Mi vyuru140)  

This article is cited in 7 scientific papers (total in 7 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

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.

DOI: https://doi.org/10.14529/mmp140301

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MSC: 35K70, 60H30
Received: 14.05.2014
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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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Zagrebina, A. S. Konkina, “The multipoint initial-final value condition for the Navier–Stokes linear model”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:1 (2015), 132–136  mathnet  crossref  elib
    2. N. A. Manakova, G. A. Sviridyuk, “Neklassicheskie uravneniya matematicheskoi fiziki. Fazovye prostranstva polulineinykh uravnenii sobolevskogo tipa”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 8:3 (2016), 31–51  mathnet  crossref  elib
    3. N. A. Manakova, “On modified method of multistep coordinate descent for optimal control problem for semilinear Sobolev-type model”, J. Comp. Eng. Math., 3:4 (2016), 59–72  mathnet  crossref  mathscinet  elib
    4. A. S. Konkina, “Stokhasticheskaya model devisa s mnogotochechnym nachalno-konechnym usloviem”, UBS, 69 (2017), 21–28  mathnet  elib
    5. N. N. Solovyova, S. A. Zagrebina, G. A. Sviridyuk, “Sobolev type mathematical models with relatively positive operators in the sequence spaces”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 9:4 (2017), 27–35  mathnet  crossref  elib
    6. G. A. Sviridyuk, A. A. Zamyshlyaeva, S. A. Zagrebina, “Multipoint initial-final problem for one class of Sobolev type models of higher order with additive “white noise””, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:3 (2018), 103–117  mathnet  crossref  elib
    7. A. O. Kondyukov, T. G. Sukacheva, “Fazovoe prostranstvo pervoi nachalno-kraevoi zadachi dlya sistemy Oskolkova vysshego poryadka”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:4 (2018), 67–77  mathnet  crossref  elib
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