Geodesic
Boundary and internal layers in the reaction-diffusion problem with a nonlocal inhibitor
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1081-1090 
N. N. Nefedov; A. G. Nikitin. Boundary and internal layers in the reaction-diffusion problem with a nonlocal inhibitor. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1081-1090. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a9/
@article{ZVMMF_2011_51_6_a9,
     author = {N. N. Nefedov and A. G. Nikitin},
     title = {Boundary and internal layers in the reaction-diffusion problem with a~nonlocal inhibitor},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1081--1090},
     year = {2011},
     volume = {51},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a9/}
}
TY  - JOUR
AU  - N. N. Nefedov
AU  - A. G. Nikitin
TI  - Boundary and internal layers in the reaction-diffusion problem with a nonlocal inhibitor
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1081
EP  - 1090
VL  - 51
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a9/
LA  - ru
ID  - ZVMMF_2011_51_6_a9
ER  - 
%0 Journal Article
%A N. N. Nefedov
%A A. G. Nikitin
%T Boundary and internal layers in the reaction-diffusion problem with a nonlocal inhibitor
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1081-1090
%V 51
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a9/
%G ru
%F ZVMMF_2011_51_6_a9

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

A nonlinear parabolic integral problem arising in dynamic simulation of processes in activator–inhibitor systems is considered. Based on the asymptotic theory of such problems previously developed by the authors, the existence of solutions with boundary and internal layers is proved and their asymptotic behavior is found.

[1] Raquepas J., Dockery J., “Dynamics of a reaction-diffusion equation with nonlocal inhibition”, Physica D, 134 (1999), 94–110 | DOI | MR | Zbl

[2] Nefedov N. N., Nikitin A. G., “Asimptoticheskii metod differentsialnykh neravenstv dlya singulyarno vozmuschennykh integrodifferentsialnykh uravnenii”, Differents. ur-niya, 36:10 (2000), 1398–1404 | MR | Zbl

[3] Nefedov N. N., Nikitin A. G., “Razvitie asimptoticheskogo metoda differentsialnykh neravenstv dlya reshenii tipa stupenki v singulyarno vozmuschennykh integrodifferentsialnykh uravneniyakh”, Zh. vychisl. matem. i matem. fiz., 41:7 (2001), 1057–1066 | MR | Zbl

[4] Nefedov N. N., Nikitin A. G., “Asimptoticheskaya ustoichivost kontrastnykh struktur tipa stupenki v singulyarno vozmuschennykh integrodifferentsialnykh uravneniyakh v dvumernom sluchae”, Matem. modelirovanie, 13:12 (2001), 65–74 | MR | Zbl

[5] Nefedov N. N., Nikitin A. G., “Metod differentsialnykh neravenstv dlya kontrastnykh struktur tipa stupenki v singulyarno vozmuschennykh integrodifferentsialnykh uravneniyakh v prostranstvenno dvumernom sluchae”, Differents. ur-niya, 42:5 (2006), 690–700 | MR | Zbl

[6] Nefedov N. N., Nikitin A. G., Recke L., Moving internal layers in the singular perturbed integro-parabolic reaction-diffusion-advection equations, Preprint No. 2007-22, Humboldt Univ., Inst. Math., Berlin, 2007, 17 pp.

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

[8] Zabreiko P. P., Koshelev A. I., Krasnoselskii M. A. i dr., Integralnye uravneniya, Nauka, M., 1968