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 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]: Year: Volume: Issue: Page: Find

 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, Issue 4(37), Pages 133–143 (Mi vsgtu1308)

Mathematical Modeling

On the question of optimization of the oil slick biodestruction in the bodies of water

O. S. Afanas'evaa, G. F. Egorovaa, L. V. Kaidalovab

a Samara State Technical University, Samara, 443100, Russian Federation
b Samara State Transport University, Samara, 443066, Russian Federation

Abstract: We propose the system of nonlinear partial differential equations of parabolic type that describes the processes of oil pollution of water surface and bacterial degradation of this contamination. Problem of the parametric optimization of the acceleration process of degradation of the oil pollution is solved using this model. Optimality criterion is to minimize the time spent on destruction of oil pollution. Coefficient, characterizing the rate of population growth of bacteria, is selected as control parameter. Research is conducted using linearization of functions from the right-hand side of an equation in the neighborhood of solutions having practical significance. Also using the simplified model we obtain the formula that allows to predict the time for necessary destruction level progressing. Checking the results obtained for the linear equations is made using MATLAB. A comparison of experimental data and the calculated values is carried on to show the suggested model adequacy.

Keywords: oil pollution, bacterial destruction, system of differential equations, linearization, Fourier method, optimization

DOI: https://doi.org/10.14498/vsgtu1308

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Bibliographic databases:

UDC: 517.958:502.51(26):504.5
MSC: Primary 93A30; Secondary 93C15, 68U20, 92D40
Original article submitted 05/IV/2014
revision submitted – 15/X/2014

Citation: O. S. Afanas'eva, G. F. Egorova, L. V. Kaidalova, “On the question of optimization of the oil slick biodestruction in the bodies of water”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 4(37) (2014), 133–143

Citation in format AMSBIB
\Bibitem{AfaEgoKai14} \by O.~S.~Afanas'eva, G.~F.~Egorova, L.~V.~Kaidalova \paper On the question of optimization of the oil slick biodestruction in the bodies of water \jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.] \yr 2014 \vol 4(37) \pages 133--143 \mathnet{http://mi.mathnet.ru/vsgtu1308} \crossref{https://doi.org/10.14498/vsgtu1308} \zmath{https://zbmath.org/?q=an:06968939}