Geodesic
Stationary internal layers in a reaction-advection-diffusion integro-differential system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 624-646

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A class of singularly perturbed nonlinear integro-differential problems with solutions involving internal transition layers (contrast structures) is considered. An asymptotic expansion of these solutions with respect to a small parameter is constructed, and the stability of stationary solutions to the associated integro-parabolic problems is investigated. The asymptotics are substantiated using the asymptotic method of differential inequalities, which is extended to the new class of problems. The method is based on well-known theorems about differential inequalities and on the idea of using formal asymptotics for constructing upper and lower solutions in singularly perturbed problems with internal and boundary layers. 
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     author = {N. N. Nefedov and O. E. Omel'chenko and L. Recke},
     title = {Stationary internal layers in a~reaction-advection-diffusion integro-differential system},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {46},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a7/}
}
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N. N. Nefedov; O. E. Omel'chenko; L. Recke. Stationary internal layers in a reaction-advection-diffusion integro-differential system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 624-646. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a7/