We study a mathematical model of the dynamics of methane isolation out of a peace of coal, which represents the initial boundary problem for the system consisting of the diffusion equation, and desorption equation. For coals of small fractions after averaging the fields of free and bounded concentrations over space variables, their definition is reduced to solving the Cauchy problem for the system of two nonlinear ordinary first-order equations. Analytic solutions of the nonaveraged and averaged corresponding linear problems are obtained.

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