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Matem. Mod., 2019, Volume 31, Number 9, Pages 101–130 (Mi mm4112)  

Nonstationary contrast structures of the problem of reaction-diffusion with roots of integral sheet in a inhomogeneous medium

A. A. Bykov, K. E. Ermakova

Lomonosov Moscow State University, Faculty of Physics, Department of Mathematics

Abstract: A description is given of contrasting structures arising from the simulation of reaction – diffusion processes in an inhomogeneous medium with a power dependence of the source density on the concentration in the vicinity of the roots. The results obtained earlier for a homogeneous medium are generalized to the case of an inhomogeneous medium, and sufficient conditions for the existence of a solution of the type of contrast structure are strictly substantiated. The exponent of the root function of the right-hand side, in contrast to previously known results, is assumed to be non-integer, including irrational. It is shown that the front (relative to the direction of movement) part of the front is an exponential function, the rear part of the front is a power function, and this is a fundamentally new, previously unknown result. The family of exact solutions of the evolution equation is found. The formal asymptotics of the solution of the initial-boundary value problem for the reaction-diffusion equation is constructed. The substantiation of the correctness of the partial sum of an asymptotic series using the method of differential inequalities is given.

Keywords: nonlinear differential equations, asymptotic methods, contrast structure, differential inequalities.

DOI: https://doi.org/10.1134/S0234087919090065

Full text: PDF file (661 kB)
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Received: 10.12.2018
Revised: 10.12.2018
Accepted:11.02.2019

Citation: A. A. Bykov, K. E. Ermakova, “Nonstationary contrast structures of the problem of reaction-diffusion with roots of integral sheet in a inhomogeneous medium”, Matem. Mod., 31:9 (2019), 101–130

Citation in format AMSBIB
\Bibitem{BykErm19}
\by A.~A.~Bykov, K.~E.~Ermakova
\paper Nonstationary contrast structures of the problem of reaction-diffusion with roots of integral sheet in a inhomogeneous medium
\jour Matem. Mod.
\yr 2019
\vol 31
\issue 9
\pages 101--130
\mathnet{http://mi.mathnet.ru/mm4112}
\crossref{https://doi.org/10.1134/S0234087919090065}
\elib{https://elibrary.ru/item.asp?id=38590309}


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