Volume I   |   Issue VIII  |   2007
Optimum Control in the Problem of Minimization of Harmful Impurities in the Atmosphere by Pontryagin’s Maximum Principle and Spherical Harmonics Method

Author(s)
R.R. Rafatov

Keywords

Cite this Article
Rafatov, R.R., (2007). Optimum Control in the Problem of Minimization of Harmful Impurities in the Atmosphere by Pontryagin’s Maximum Principle and Spherical Harmonics Method, Manas Journal of Engineering Science (MJES), 1(8), pp: 33-54

Abstract
Protection of the environment from the industrial pollution is one of the most actual problems of modern science and engineering. This paper is devoted to the investigation of the problem, related to the disposition of industrial objects, which provides the minimal pollution of nearby economically important objects. It is supposed that all of the industrial objects in the given region throw out respective quantities of the harmful impurity in the atmosphere. The problem consist of the determining for each of the industrial object of such admissible amount of harmful impurity, which provide the minimum for the integral of their squares. At the same time, the density of the harmful particles must be as much as possible close, on the average, to the sanitary allowable norms.

References
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[3] Sultangazin U M 2001 Bulletin of KGNU on Mathematical and Computer Sciences (KGNU, Bishkek) 5 15 (in Russian)

[4] Sultangazin U M 1979 Methods of Spherical Harmonics and Discrete Ordinates in the Problems of Kinetic Transport (Alma-Ata, USSR: Nauka) (in Russian)

[5] Case K. M. and Zweifel P. F. 1972 Linear Transport Theory (Moscow: Mir) (in Russian)

[6] Rafatov R. R. 2002 J Natural Sciences (Kyrgyz-Turkish University ‘Manas’, Bishkek) 2 96 (in Russian)

[7] Marchuk G. I. 1982 Mathematical Modeling in Environmental Problems (Moscow: Nauka) (in Russian)

[8] Egorov A I 1978 Optimal Control in Thermal and Diffusion Processes (Moscow: Nauka) (in Russian)

[9] Rafatov R 2004 Math Comp Simulation 67 379

 

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