Vestnik YuUrGU. Ser. Mat. Model. Progr., 2015, Volume 8, Issue 4, Pages 120–126
This article is cited in 3 scientific papers (total in 3 papers)
Optimal control for a mathematical model of nerve impulse spreading
N. A. Manakova, O. V. Gavrilova
South Ural State University, Chelyabinsk, Russian Federation
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.
Sobolev type equations; optimal control; diffusion-reaction equations.
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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
\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.
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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
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
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
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