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.
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”, Mat. Model., 31:9 (2019), 101–130; Math. Models Comput. Simul., 12:3 (2020), 329–347
\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 Mat. Model.
\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}
\transl
\jour Math. Models Comput. Simul.
\yr 2020
\vol 12
\issue 3
\pages 329--347
\crossref{https://doi.org/10.1134/S2070048220030114}
Linking options:
https://www.mathnet.ru/eng/mm4112
https://www.mathnet.ru/eng/mm/v31/i9/p101
This publication is cited in the following 2 articles:
A. A. Bykov, “Two-dimensional transient contrasting structure evolution in an inhomogeneous media with the advection”, VMU, 2024, no. №2_2024, 2420101–1
A. A. Bykov, “Evolution of a Two-Dimensional Moving Contrast Structure in an Inhomogeneous Medium with Advection”, Moscow Univ. Phys., 79:2 (2024), 140