Geodesic
Internal layers in the one-dimensional reaction–diffusion equation with a discontinuous reactive term
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2042-2048

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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. 
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     author = {N. N. Nefedov and Minkang Ni},
     title = {Internal layers in the one-dimensional reaction{\textendash}diffusion equation with a discontinuous reactive term},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2042--2048},
     publisher = {mathdoc},
     volume = {55},
     number = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a6/}
}
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N. N. Nefedov; Minkang Ni. Internal layers in the one-dimensional reaction–diffusion equation with a discontinuous reactive term. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 12, pp. 2042-2048. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_12_a6/