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Exact solutions of nonlinear sets of equations of the theory of heat and mass transfer in reactive media and mathematical biology

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Abstract

New classes of exact solutions of nonlinear sets of equations of the theory of heat and mass transfer in reactive media and mathematical biology are described. Various sets of the general form are considered, in which the chemical reaction rates depend on two or three arbitrary functions. Among the exact solutions obtained are solutions with ordinary, generalized, and functional separation of variables; time-periodic solutions; solutions that are periodic in the spatial coordinate; etc. A number of solutions contain arbitrary functions (they are expressed in terms of solutions of the linear heat equation and solutions of sets of ordinary differential equations). Sets describing the multicomponent reaction-diffusion and also some sets in several spatial variables are studied.

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Authors and Affiliations

  1. Institute of Problems of Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101/1, 117526, Moscow, Russia

    A. D. Polyanin

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  1. A. D. Polyanin
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Translated from Teoreticheskie Osnovy Khimicheskoi Tekhnologii, Vol. 38, No. 6, 2004, pp. 661–674.

Original Russian Text Copyright © 2004 by Polyanin.

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Polyanin, A.D. Exact solutions of nonlinear sets of equations of the theory of heat and mass transfer in reactive media and mathematical biology. Theor Found Chem Eng 38, 622–635 (2004). https://doi.org/10.1007/s11236-005-0035-2

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  • DOI: https://doi.org/10.1007/s11236-005-0035-2

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