Non-uniqueness of the solution of one mathematical model of an autocatalytic reaction with diffusion and the Showalter – Sidorov condition

The article is devoted to the numerical study of the phase space of one mathematical model of an autocatalytic reaction with diffusion, based on a degenerate system of equations for a distributed brusselator. We will obtain conditions for the existence, uniqueness or multiplicity of solutions to the...

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Bibliographic Details
Published in:Journal of physics. Conference series 2021-03, Vol.1847 (1), p.12003
Main Authors: Gavrilova, O V, Manakova, N A
Format: Article
Language:English
Subjects:
Algorithms
Differential equations
Mathematical models
Model testing
Physics
Uniqueness
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Summary:The article is devoted to the numerical study of the phase space of one mathematical model of an autocatalytic reaction with diffusion, based on a degenerate system of equations for a distributed brusselator. We will obtain conditions for the existence, uniqueness or multiplicity of solutions to the Showalter – Sidorov problem and reveal the dependence of these conditions on the parameters of the system. The approach used in the numerical research of this problem is based on the reduction of the semilinear Sobolev-type equation to a system of algebraic-differential equations with the subsequent solution of this system using the Runge – Kutta method of order 4-5. The article also provides the result of a computational experiment which illustrates the operation of a program complex based on an algorithm for the numerical solution of the problem. The results of numerical simulation in the case of existence of two solutions of the investigated model are presented.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1847/1/012003