This article is cited in 35 papers

Internal layers in the one-dimensional reaction–diffusion equation with a discontinuous reactive term

N. N. Nefedov^a, Minkang Ni<sup>b

a</sup> 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 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.

UDC: 519.633

Received: 03.03.2015

DOI: 10.7868/S0044466915120133

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:12, 2001–2007

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