Abstract:
A wide class of mathematical physics problems can be considered within the framework of semi-linear Sobolev type equations, which describe various processes (for example deformation processes, processes occurring in semiconductors, processes of oscillatory motion propagation in various media, and so on). The article is devoted to the study of control problems (optimal, start and rigid) of one mathematical model of Sobolev type, which is based on the equation describing the process of changing the concentration potential of a viscoelastic fluid filtered in a porous medium (the process of nonlinear diffusion of matter). We find the sufficient conditions under which there exists a solution to the control problem of the model under study. An algorithm for the numerical solution method is constructed and a computational experiment is presented.
Keywords:
Sobolev type equations, nonlinear diffusion model, start control problem, optimal control problem, the problem of rigid control, mathematical modeling, projection method, decomposition method.
This work was funded by RFBR and Chelyabinsk Region, project number 20-41-740023.
Received: 15.03.2021
Document Type:
Article
UDC:
517.9
Language: English
Citation:
K. V. Perevozhikova, N. A. Manakova, A. S. Kuptsova, “Investigation of various types of control problems for one nonlinear model of filtration”, J. Comp. Eng. Math., 8:4 (2021), 45–61
\Bibitem{PerManKup21}
\by K.~V.~Perevozhikova, N.~A.~Manakova, A.~S.~Kuptsova
\paper Investigation of various types of control problems for one nonlinear model of filtration
\jour J. Comp. Eng. Math.
\yr 2021
\vol 8
\issue 4
\pages 45--61
\mathnet{http://mi.mathnet.ru/jcem204}
\crossref{https://doi.org/10.14529/jcem210406}
Linking options:
https://www.mathnet.ru/eng/jcem204
https://www.mathnet.ru/eng/jcem/v8/i4/p45
This publication is cited in the following 1 articles:
K. V. Perevozchikova, N. A. Manakova, O. V. Gavrilova, I. M. Manakov, “Algoritm chislennogo metoda nakhozhdeniya resheniya matematicheskoi modeli nelineinoi filtratsii so sluchainym nachalnym usloviem Shouoltera – Sidorova”, J. Comp. Eng. Math., 9:2 (2022), 39–51
Citation in format AMSBIB
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