Geodesic
On the formation of sharp transition layers in two-dimensional reaction-diffusion models
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 8, pp. 1356-1364 
V. T. Volkov; N. E. Grachëv; N. N. Nefedov; A. N. Nikolaev. On the formation of sharp transition layers in two-dimensional reaction-diffusion models. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 8, pp. 1356-1364. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_8_a7/
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     title = {On the formation of sharp transition layers in two-dimensional reaction-diffusion models},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_8_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a singularly perturbed parabolic equation in two dimensions, the formation of a solution with a sharp transition layer from a sufficiently general initial function is considered. An asymptotic analysis is used to estimate the time required for the formation of a contrast structure. Numerical results are presented.

[1] Vasileva A. B., Butuzov V. F., Nefedov H. H., “Kontrastnye struktury v singulyarno vozmuschennykh zadachakh”, Fundamentalnaya i prikl. matem., 4:3 (1998), 799–851 | MR

[2] Nefedov H. H., “Asimptoticheskii metod differentsialnykh neravenstv v issledovanii periodicheskikh kontrastnykh struktur: suschestvovanie, asimptotika, ustoichivost”, Differents. ur-niya, 36:2 (2000), 262–269 | MR | Zbl

[3] Nefedov N. N., Radzinus M., Schneider K. R., Vaseil'eva A. B., “Change of the type of contrast structures in parabolic Neumann Problems”, Zh. vychisl. matem. i matem. fiz., 45:1 (2005), 41–55 | MR | Zbl

[4] Butuzov V. F., Nedelko I. V., “O globalnoi oblasti vliyaniya ustoichivykh reshenii s vnutrennimi sloyami”, Matem. sb., 192:5 (2001), 13–52 | MR

[5] Butuzov V. F., Nefedov H. H., Shnaider K. P., “O formirovanii i rasprostranenii rezkikh perekhodnykh sloev v parabolicheskikh zadachakh”, Vestn. MGU. Ser. 3. Fiz. Astron., 2005, no. 1, 9–13 | MR | Zbl

[6] Allen S. M., Cohn J. W., “A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening”, Acta Metal., 27 (1979), 1085–1095 | DOI