Geodesic
Contrast structures in the reaction-diffusion-advection equations in the case of balanced advection
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 3, pp. 365-376

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For a singularly perturbed parabolic equation termed in applications as the reaction-diffusion-advection equation, stationary solutions with internal transition layers (contrast structures) are studied. An arbitrary-order asymptotic approximation of such solutions is constructed, and an existence theorem is proved. An efficient algorithm for constructing an asymptotic approximation of the transition point is proposed. The constructed asymptotic approximation is justified by applying the asymptotic method of differential inequalities, which is extended to the class of problems under study. This method is also used to establish the Lyapunov stability of such stationary solutions. 
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     author = {N. T. Levashova and N. N. Nefedov and A. V. Yagremtsev},
     title = {Contrast structures in the reaction-diffusion-advection equations in the case of balanced advection},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {365--376},
     publisher = {mathdoc},
     volume = {53},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_3_a5/}
}
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N. T. Levashova; N. N. Nefedov; A. V. Yagremtsev. Contrast structures in the reaction-diffusion-advection equations in the case of balanced advection. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 3, pp. 365-376. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_3_a5/