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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2015, Volume 8, Issue 3, Pages 5–24 (Mi vyuru273)  

This article is cited in 2 scientific papers (total in 3 papers)

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Mathematical models and optimal control of the filtration and deformation processes

N. A. Manakova

South Ural State University, Chelyabinsk, Russian Federation

Abstract: The article presents a review author's works on study of optimal control problems for semilinear Sobolev type models with $s$-monotone and $p$-coercive operators. Theorems of existence and uniqueness of weak generalized solution to the Cauchy or the Showalter–Sidorov problem for a class of degenerate non-classical models of mathematical physics are stated. The theory is based on the phase space and the Galerkin–Petrov methods. The developed scheme of a numerical method allows one to find an approximate solution to the Cauchy or Showalter–Sidorov problems for considered models. An abstract scheme for study of the optimal control problem for this class of models is constructed. On the basis of abstract results the existence of optimal control of processes of filtration and deformation are obtained. The necessary conditions for optimal control are provided.

Keywords: Sobolev type equations; optimal control; phase space method; Galerkin–Petrov method.

DOI: https://doi.org/10.14529/mmp150301

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Bibliographic databases:

UDC: 517.9
MSC: 35K70
Received: 15.04.2015

Citation: N. A. Manakova, “Mathematical models and optimal control of the filtration and deformation processes”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:3 (2015), 5–24

Citation in format AMSBIB
\Bibitem{Man15}
\by N.~A.~Manakova
\paper Mathematical models and optimal control of the filtration and deformation processes
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2015
\vol 8
\issue 3
\pages 5--24
\mathnet{http://mi.mathnet.ru/vyuru273}
\crossref{https://doi.org/10.14529/mmp150301}
\elib{http://elibrary.ru/item.asp?id=24078392}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. M. Buryak, T. K. Plyshevskaya, A. B. Samarov, “Seminaru po uravneniyam sobolevskogo tipa chetvert veka”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 10:1 (2017), 165–169  mathnet  crossref  elib
    2. N. A. Manakova, K. V. Vasiuchkova, “Numerical investigation for the start control and final observation problem in model of an I-beam deformation”, J. Comp. Eng. Math., 4:2 (2017), 26–40  mathnet  crossref  mathscinet  elib
    3. 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
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