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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 12, Pages 2042–2048 (Mi zvmmf10313)  

This article is cited in 7 scientific papers (total in 7 papers)

Internal layers in the one-dimensional reactiondiffusion equation with a discontinuous reactive term

N. N. Nefedova, Minkang Nib

a Faculty of Physics, Moscow State University, Moscow, 119991, Russia
b East China Normal University, Shanghai, 200241, People's Republic of China

Abstract: A singularly perturbed boundary value problem for a second-order ordinary differential equation known in applications as a stationary reactiondiffusion equation is studied. A new class of problems is considered, namely, problems with nonlinearity having discontinuities localized in some domains, which leads to the formation of sharp transition layers in these domains. The existence of solutions with an internal transition layer is proved, and their asymptotic expansion is constructed.

Key words: singular perturbations, one-dimensional reactiondiffusion equation, internal layers, asymptotic methods.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00200_
11471118
30921064
90820307
Chinese Academy of Sciences


DOI: https://doi.org/10.7868/S0044466915120133

Full text: PDF file (99 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:12, 2001–2007

Bibliographic databases:

UDC: 519.633
Received: 03.03.2015

Citation: N. N. Nefedov, Minkang Ni, “Internal layers in the one-dimensional reactiondiffusion equation with a discontinuous reactive term”, Zh. Vychisl. Mat. Mat. Fiz., 55:12 (2015), 2042–2048; Comput. Math. Math. Phys., 55:12 (2015), 2001–2007

Citation in format AMSBIB
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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, O. A. Nikolaeva, “Asimptoticheskoe issledovanie resheniya uravneniya teploprovodnosti vblizi granitsy razdela dvukh sred”, Model. i analiz inform. sistem, 24:3 (2017), 339–352  mathnet  crossref  elib
    2. N. T. Levashova, N. N. Nefedov, A. O. Orlov, “Time-independent reaction-diffusion equation with a discontinuous reactive term”, Comput. Math. Math. Phys., 57:5 (2017), 854–866  mathnet  crossref  crossref  mathscinet  isi  elib
    3. M. Ni, Ya. Pang, N. T. Levashova, O. A. Nikolaeva, “Internal layers for a singularly perturbed second-order quasilinear differential equation with discontinuous right-hand side”, Differ. Equ., 53:12 (2017), 1567–1577  crossref  mathscinet  zmath  isi
    4. Yafei Pan, Min Kan Ni, M. A. Davydova, “Contrast Structures in Problems for a Stationary Equation of Reaction-Diffusion-Advection Type with Discontinuous Nonlinearity”, Math. Notes, 104:5 (2018), 735–744  mathnet  crossref  crossref  isi  elib
    5. Pang Yafei, Ni Mingkang, N. T. Levashova, “Internal layer for a system of singularly perturbed equations with discontinuous right-hand side”, Differ. Equ., 54:12 (2018), 1583–1594  crossref  mathscinet  isi  scopus
    6. N. N. Nefedov, N. T. Levashova, A. O. Orlov, “The asymptotic stability of a stationary solution with an internal transition layer to a reaction-diffusion problem with a discontinuous reactive term”, Mosc. Univ. Phys. Bull., 73:6 (2018), 565–572  crossref  isi  scopus
    7. Qi X. Ni M., “On the Asymptotic Solution to a Type of Piecewise-Continuous Second-Order Dirichlet Problems of Tikhonov System”, J. Appl. Anal. Comput., 9:1 (2019), 105–117  crossref  isi
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