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Zh. Vychisl. Mat. Mat. Fiz., 2018, Volume 58, Number 5, Pages 705–715 (Mi zvmmf10731)  

Existence and asymptotic representation of the autowave solution of a system of equations

A. A. Melnikova, M. Chen

Physical Faculty, Moscow State University, Moscow, Russia

Abstract: A singularly perturbed parabolic system of nonlinear reaction-diffusion equations is studied. Systems of this class are used to simulate autowave processes in chemical kinetics, biophysics, and ecology. A detailed algorithm for constructing an asymptotic approximation of a travelling front solution is proposed. In addition, methods for constructing an upper and a lower solution based on the asymptotics are described. According to the method of differential inequalities, the existence of an upper and a lower solution guarantees the existence of a solution to the problem under consideration. These methods can be used for asymptotic analysis of model systems in applications. The results can also be used to develop and justify difference schemes for solving problems with moving fronts.

Key words: system of reaction-diffusion equations, small parameter, internal transition layer, method of differential inequalities, contrast structures.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-04619_а
16-01-00437_а


DOI: https://doi.org/10.7868/S0044466918050034

References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2018, 58:5, 680–690

Bibliographic databases:

UDC: 519.633
Received: 13.02.2017

Citation: A. A. Melnikova, M. Chen, “Existence and asymptotic representation of the autowave solution of a system of equations”, Zh. Vychisl. Mat. Mat. Fiz., 58:5 (2018), 705–715; Comput. Math. Math. Phys., 58:5 (2018), 680–690

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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