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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 12, Pages 2042–2048
DOI: https://doi.org/10.7868/S0044466915120133 (Mi zvmmf10313) 		 
This article is cited in 32 scientific papers (total in 32 papers)

Internal layers in the one-dimensional reaction–diffusion 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
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DOI: https://doi.org/10.7868/S0044466915120133
Abstract: A singularly perturbed boundary value problem for a second-order ordinary differential equation known in applications as a stationary reaction–diffusion 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 reaction–diffusion equation, internal layers, asymptotic methods.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00200_à
Ïðîåêò ÔÃÅÍ 11471118
Ïðîåêò ÔÃÅÍ 30921064
Ïðîåêò ÔÃÅÍ 90820307
Chinese Academy of Sciences
Received: 03.03.2015
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 12, Pages 2001–2007
DOI: https://doi.org/10.1134/S096554251512012X
Bibliographic databases:
Document Type: Article
UDC: 519.633
Language: Russian
Citation: N. N. Nefedov, Minkang Ni, “Internal layers in the one-dimensional reaction–diffusion 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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    • This publication is cited in the following 32 articles:
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    		Æóðíàë âû÷èñëèòåëüíîé ìàòåìàòèêè è ìàòåìàòè÷åñêîé ôèçèêè Computational Mathematics and Mathematical Physics
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