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The solution with internal transition layer of the reaction‐diffusion equation in case of discontinuous reactive and diffusive terms
Author(s) -
Levashova Natalia T.,
Nefedov Nikolay N.,
Nikolaeva Olga A.,
Orlov Andrey O.,
Panin Alexander A.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5134
Subject(s) - mathematics , transition layer , discontinuity (linguistics) , mathematical analysis , initial value problem , diffusion , reaction–diffusion system , boundary layer , transition point , boundary value problem , differential equation , diffusion equation , stability (learning theory) , layer (electronics) , thermodynamics , physics , chemistry , economy , organic chemistry , economics , service (business) , machine learning , computer science
In this paper, we use the asymptotical analysis to construct the asymptotic approximation of the solution with internal transition layer of the boundary value problem for a reaction‐diffusion equation on the segment in case of discontinuous reactive and diffusive terms. The internal layer is located in the vicinity of a single point of discontinuity of the mentioned terms. We also investigate the existence and stability of such solution. For the last purpose, we use the asymptotical method of differential inequalities.