Geodesic
On the stability of a steplike contrast structure for a parabolic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 3, pp. 448-461 
A. B. Vasil'eva; E. E. Bukzhalev. On the stability of a steplike contrast structure for a parabolic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 3, pp. 448-461. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_3_a9/
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     title = {On the stability of a steplike contrast structure for a parabolic equation},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Solutions to a singularly perturbed parabolic equation are constructed that have internal and boundary layers with stretched variables depending on various powers of a perturbation parameter. Asymptotics of one of these solutions is constructed, and its stability is analyzed.

[1] Bukzhalev E. E., “Kontrastnye struktury tipa stupenki, rastyanutye peremennye kotorykh zavisyat ot razlichnykh stepenei parametra vozmuscheniya”, Zh. vychisl. matem. i matem. fiz., 44:4 (2004), 662–675 | MR | Zbl

[2] Vasileva A. B., Butuzov V. F., Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Vyssh. shkola, M., 1990 | MR

[3] 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

[4] Vasileva A. B., Davydova M. A., “Singulyarno vozmuschennoe uravnenie vtorogo poryadka s malymi parametrami pri pervoi i vtoroi proizvodnykh”, Zh. vychisl. matem. i matem. fiz., 39:9 (1999), 1504–1512 | MR

[5] Bukzhalev E. E., “Singulyarno vozmuschennoe uravnenie s pogransloinym resheniem, rastyanutye peremennye kotorogo zavisyat ot razlichnykh stepenei parametra vozmuscheniya”, Zh. vychisl. matem. i matem. fiz., 43:12 (2003), 1775–1785 | MR | Zbl

[6] Amann H., “Periodic solutions of semi-linear parabolic equations”, Nonlinear Analysis, A Collection of Papers in Honor of Erich Rothe, Acad. Press, New York, 1978, 1–29 | MR

[7] Bukzhalev E. E., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh differentsialnykh uravnenii vtorogo poryadka v razlichnykh sluchayakh zavisimosti pravoi chasti ot pervoi proizvodnoi, Dis. ...kand. fiz.-matem. nauk, MGU, M., 2004

[8] Kolesov Yu. S., “O nekotorykh priznakakh suschestvovaniya ustoichivykh periodicheskikh reshenii u kvazilineinykh parabolicheskikh uravnenii”, Dokl. AN SSSR, 157:6 (1964), 1288–1290 | MR | Zbl

[9] Butuzov V. F., Nedelko I. V., “Ustoichivost kontrastnykh struktur tipa stupenki v dvumernom sluchae”, Dokl. RAN, 366:3 (1999), 1–4 | MR

[10] Butuzov V. F., Nedelko I. V., “O globalnoi oblasti vliyaniya reshenii s vnutrennimi sloyami”, Dokl. RAN, 373:2 (2000), 155–156 | MR | Zbl

[11] Butuzov V. F., Nedelko I. V., “O globalnoi oblasti vliyaniya ustoichivykh reshenii s vnutrennimi sloyami v dvumernom sluchae”, Izv. RAN. Ser. matem., 66:1 (2002), 3–42 | MR | Zbl

[12] Vasileva A. B., Omelchenko O. E., “Periodicheskie kontrastnye struktury tipa stupenki dlya singulyarno vozmuschennogo parabolicheskogo uravneniya”, Differents. ur-niya, 36:2 (2000), 198–208 | MR