This article is cited in 7 scientific papers (total in 7 papers)
Solution with an inner transition layer of a two-dimensional boundary value reaction–diffusion–advection problem with discontinuous reaction and advection terms
Abstract:
We study the problem of the existence and asymptotic stability of a stationary solution of an initial boundary value problem for the reaction–diffusion–advection equation assuming that the reaction and advection terms are comparable in size and have a jump along a smooth curve located inside the studied domain. The problem solution has a large gradient in a neighborhood of this curve. We prove theorems on the existence, asymptotic uniqueness, and Lyapunov asymptotic stability for such solutions using the method of upper and lower solutions. To obtain the upper and lower solutions, we use the asymptotic method of differential inequalities that consists in constructing them as modified asymptotic approximations in a small parameter of solutions of these problems. We construct the asymptotic approximation of a solution using a modified Vasil'eva method.
Keywords:
reaction–diffusion–advection equation, discontinuous term, method of differential inequalities, upper solution, lower solution, inner transition layer, small parameter.
Citation:
N. T. Levashova, N. N. Nefedov, O. A. Nikolaeva, “Solution with an inner transition layer of a two-dimensional boundary value reaction–diffusion–advection problem with discontinuous reaction and advection terms”, TMF, 207:2 (2021), 293–309; Theoret. and Math. Phys., 207:2 (2021), 655–669
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\paper Solution with an inner transition layer of a~two-dimensional boundary value reaction--diffusion--advection problem with discontinuous reaction and advection terms
\jour TMF
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\pages 293--309
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\jour Theoret. and Math. Phys.
\yr 2021
\vol 207
\issue 2
\pages 655--669
\crossref{https://doi.org/10.1134/S0040577921050093}
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Linking options:
https://www.mathnet.ru/eng/tmf10032
https://doi.org/10.4213/tmf10032
https://www.mathnet.ru/eng/tmf/v207/i2/p293
This publication is cited in the following 7 articles:
E. I. Nikulin, B. T. Volkov, D. A. Karmanov, “Periodic Inner Transition Layers in the Reaction–Diffusion Problem in the Case of Weak Reaction Discontinuity”, VMU, 80:№1, 2025 (2025)
E. I. Nikulin, V. T. Volkov, D. A. Karmanov, “Internal Transition Layer Structure
in the Reaction–Diffusion Problem for the Case
of a Balanced Reaction with a Weak Discontinuity”, Diff Equat, 60:1 (2024), 65
E. I Nikulin, V. T Volkov, D. A Karmanov, “STRUKTURA VNUTRENNEGO PEREKhODNOGO SLOYa V ZADAChE REAKTsIYa–DIFFUZIYa V SLUChAE SBALANSIROVANNOY REAKTsII SO SLABYM RAZRYVOM”, Differencialʹnye uravneniâ, 60:1 (2024), 64
N. N. Nefedov, E. I. Nikulin, A. O. Orlov, “Contrast structures in the reaction-diffusion-advection problem in the case of a weak reaction discontinuity”, Russ. J. Math. Phys., 29:1 (2022), 81
N. N. Nefedov, E. I. Nikulin, A. O. Orlov, “Existence of contrast structures in a problem with discontinuous reaction and advection”, Russ. J. Math. Phys., 29:2 (2022), 214
N. N. Nefedov, “Development of methods of asymptotic analysis of transition layers in reaction–diffusion–advection equations: theory and applications”, Comput. Math. Math. Phys., 61:12 (2021), 2068–2087
Citation in format AMSBIB
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