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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 4, Pages 611–620 (Mi zvmmf10879)  

This article is cited in 1 scientific paper (total in 1 paper)

Asymptotic stability of a stationary solution of a multidimensional reaction-diffusion equation with a discontinuous source

N. T. Levashova, N. N. Nefedov, A. O. Orlov

Lomonosov Moscow State University, Moscow, 119992 Russia

Abstract: A two-dimensional reaction-diffusion equation in a medium with discontinuous characteristics is considered; the existence, local uniqueness, and asymptotic stability of its stationary solution, which has a large gradient at the interface, is proved. This paper continues the authors' works concerning the existence and stability of solutions with internal transition layers of boundary value problems with discontinuous terms to multidimensional problems. The proof of the existence and stability of a solution is based on the method of upper and lower solutions. The methods of analysis proposed in this paper can be generalized to equations of arbitrary dimension of the spatial variables, as well as to more complex problems, e.g., problems for systems of equations. The results of this work can be used to develop numerical algorithms for solving stiff problems with discontinuous coefficients.

Key words: reactionЦdiffusion problem, internal layers, asymptotics of solution, Lyapunov asymptotic stability, comparison principle.

Funding Agency Grant Number
Russian Science Foundation 18-11-00042
This work was supported by the Russian Science Foundation, project no. 18-11-00042.


DOI: https://doi.org/10.1134/S0044466919040100


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:4, 573–582

Bibliographic databases:

UDC: 517.958
Received: 19.09.2018
Revised: 14.11.2018
Accepted:14.11.2018

Citation: N. T. Levashova, N. N. Nefedov, A. O. Orlov, “Asymptotic stability of a stationary solution of a multidimensional reaction-diffusion equation with a discontinuous source”, Zh. Vychisl. Mat. Mat. Fiz., 59:4 (2019), 611–620; Comput. Math. Math. Phys., 59:4 (2019), 573–582

Citation in format AMSBIB
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\paper Asymptotic stability of a stationary solution of a multidimensional reaction-diffusion equation with a discontinuous source
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2019
\vol 59
\issue 4
\pages 611--620
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\crossref{https://doi.org/10.1134/S0044466919040100}
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\transl
\jour Comput. Math. Math. Phys.
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\pages 573--582
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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”, Theoret. and Math. Phys., 207:2 (2021), 655–669  mathnet  crossref  crossref  isi
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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