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<p>We consider a system of equations that describes a two-component chemical reaction in a limited volume. The reaction is assumed to occur in a solution, the concentration of reaction products increases in time, then becomes maximal possible under the given conditions (i.e., saturation occurs), and then the reaction terminates. A similar formulation can be used for describing microscopic processes occurring when CO<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation> is injected into a rock, which is a porous medium with pores filled with water. For a system of two equations of the “reaction-diffusion” type on a segment, we show that in a finite time, a solution close to a stationary distribution corresponding to the concentration of a saturated solution under given conditions is formed from a given initial function.</p>

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FORMATION OF A BOUNDARY-LAYER SOLUTION IN A PROBLEM FOR A SYSTEM OF REACTION-DIFFUSION EQUATIONS IN A LIMITED VOLUME

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • N. T. Levashova

摘要

We consider a system of equations that describes a two-component chemical reaction in a limited volume. The reaction is assumed to occur in a solution, the concentration of reaction products increases in time, then becomes maximal possible under the given conditions (i.e., saturation occurs), and then the reaction terminates. A similar formulation can be used for describing microscopic processes occurring when CO \(_2\) 2 is injected into a rock, which is a porous medium with pores filled with water. For a system of two equations of the “reaction-diffusion” type on a segment, we show that in a finite time, a solution close to a stationary distribution corresponding to the concentration of a saturated solution under given conditions is formed from a given initial function.