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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2015, Volume 8, Issue 4, Pages 120–126 (Mi vyuru294)  

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

Short Notes

Optimal control for a mathematical model of nerve impulse spreading

N. A. Manakova, O. V. Gavrilova

South Ural State University, Chelyabinsk, Russian Federation

Abstract: The article concerns the matter of existence of optimal control for the mathematical model set forward by R. Fitzhugh and J. M. Nagumo for modelling of nerve impulse spreading. The model belongs to the group of diffusion-reaction models simulating a wide range of processes such as chemical reactions with diffusion and nerve impulse spreading. In case, that there is an asymptotical stability of the studied model, and under an assumption that the rate of variation of one component is greatly higher than the other one, the said model could be reduced to a problem of optimal control of a Sobolev type semi-linear equation with Showalter–Sidorov initial condition. The article contents a demonstration of the only weak generalized solution for the model under discussion with Showalter–Sidorov initial condition and optimal control existence.

Keywords: Sobolev type equations; optimal control; diffusion-reaction equations.

DOI: https://doi.org/10.14529/mmp150411

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Bibliographic databases:

UDC: 517.9
MSC: 49J20
Received: 15.06.2015

Citation: N. A. Manakova, O. V. Gavrilova, “Optimal control for a mathematical model of nerve impulse spreading”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 8:4 (2015), 120–126

Citation in format AMSBIB
\Bibitem{ManGav15}
\by N.~A.~Manakova, O.~V.~Gavrilova
\paper Optimal control for a mathematical model of nerve impulse spreading
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2015
\vol 8
\issue 4
\pages 120--126
\mathnet{http://mi.mathnet.ru/vyuru294}
\crossref{https://doi.org/10.14529/mmp150411}
\elib{http://elibrary.ru/item.asp?id=24989388}


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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. 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
    2. O. V. Gavrilova, “Zadacha startovogo upravleniya i finalnogo nablyudeniya dlya sistemy uravnenii Fitts Khyu–Nagumo s usloviem Dirikhle–Shouoltera–Sidorova”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 10:3 (2018), 12–18  mathnet  crossref  elib
    3. N. A. Manakova, O. V. Gavrilova, “About nonuniqueness of solutions of the Showalter–Sidorov problem for one mathematical model of nerve impulse spread in membrane”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 11:4 (2018), 161–168  mathnet  crossref  elib
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