A controlled model of the carbon cycle in the biosphere allowing for human activity on a global scale was developed by Kryazhimskii using the results of Svirezhev et al. The present article is a mathematical study of Kryazhimskii’s model. In the first part we calculate the supremum for t ≥ 0 of the function x(t)—the quantity of carbon in the atmosphere as a function of varying initial conditions and coefficients in the corresponding differential equations. In the second part we consider the problem of minimizing the economic costs of reducing carbon emissions to a level that meets given constraints on carbon concentration in the atmosphere. The penalty method is applied to determine the structure of one of the optimal controls for a particular case relevant in practice. This special optimal control has at most one switching point and everywhere takes one of its two extreme values (a relay mode).
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Translated from Nelineinaya Dinamika i Upravlenie, No. 5, pp. 251–262, 2006.
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M. S. Nikol’skii. A controlled model of carbon circulation between the atmosphere and the ocean. Comput Math Model 21, 414–424 (2010). https://doi.org/10.1007/s10598-010-9081-7
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DOI: https://doi.org/10.1007/s10598-010-9081-7