Geodesic
Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reaction-diffusion equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 615-623 
V. T. Volkov; N. N. Nefedov. Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reaction-diffusion equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 4, pp. 615-623. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a6/
@article{ZVMMF_2006_46_4_a6,
     author = {V. T. Volkov and N. N. Nefedov},
     title = {Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reaction-diffusion equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {615--623},
     year = {2006},
     volume = {46},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a6/}
}
TY  - JOUR
AU  - V. T. Volkov
AU  - N. N. Nefedov
TI  - Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reaction-diffusion equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 615
EP  - 623
VL  - 46
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a6/
LA  - ru
ID  - ZVMMF_2006_46_4_a6
ER  - 
%0 Journal Article
%A V. T. Volkov
%A N. N. Nefedov
%T Development of the asymptotic method of differential inequalities for investigation of periodic contrast structures in reaction-diffusion equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 615-623
%V 46
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_4_a6/
%G ru
%F ZVMMF_2006_46_4_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

The asymptotical method of differential inequalities is developed for a new class of periodic problems of reaction-diffusion type. The problem of the existence and Lyapunov stability of periodic solutions with internal transient layers in the case of balanced nonlinearity is studied.

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

[2] Vasileva A. B., Omelchenko O. E., “Periodicheskie kontrastnye struktury tipa stupenki dlya singulyarno vozmuschennogo parabolicheskogo uravneniya”, Differents. ur-niya, 36:2 (2000), 209–218 | MR

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

[4] Volkov V. T., Nefedov H. H., “O periodicheskikh resheniyakh s pogranichnymi sloyami odnoi singulyarno vozmuschennoi modeli reaktsiya-diffuziya”, Zh. vychisl. matem. i matem. fiz., 34:8 (1994), 1307–1315 | MR | Zbl

[5] Amman H., Periodic solutions of semilinear parabolic equations in nonlinear analysis, Acad. Press, New York, 1978 | MR

[6] Nefedov H. H., “Metod differentsialnykh neravenstv dlya nekotorykh klassov nelineinykh singulyarno vozmuschennykh zadach s vnutrennimi sloyami”, Differents. ur-niya, 31:7 (1995), 1142–1149 | MR | Zbl

[7] Pao C. V., Nonlinear parabolic and elliptic equations, Plenum Press, New York, London, 1992 | MR