Geodesic
Asymptotic analysis of integro-differential systems with an unstable spectral value of the integral operator's kernel
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 67-82

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

A system of integro-differential equations with rapidly varying kernels, one of which has an unstable spectral value, is considered. An algorithm based on the method of normal forms is proposed for finding asymptotic solutions (of an arbitrary order). The contrast structures (internal transition layers) in solutions to the problem are investigated by analyzing the leading term of the asymptotic expansion. It is shown that the contrast structures are caused by the instability of the spectral value and by the presence of inhomogeneity. The role of the kernels of the integral operators in the formation of contrast structures is clarified. 
@article{ZVMMF_2007_47_1_a7,
     author = {A. A. Bobodzhanov and V. F. Safonov},
     title = {Asymptotic analysis of integro-differential systems with an unstable spectral value of the integral operator's kernel},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {67--82},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a7/}
}
TY  - JOUR
AU  - A. A. Bobodzhanov
AU  - V. F. Safonov
TI  - Asymptotic analysis of integro-differential systems with an unstable spectral value of the integral operator's kernel
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 67
EP  - 82
VL  - 47
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a7/
LA  - ru
ID  - ZVMMF_2007_47_1_a7
ER  - 
%0 Journal Article
%A A. A. Bobodzhanov
%A V. F. Safonov
%T Asymptotic analysis of integro-differential systems with an unstable spectral value of the integral operator's kernel
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 67-82
%V 47
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a7/
%G ru
%F ZVMMF_2007_47_1_a7
A. A. Bobodzhanov; V. F. Safonov. Asymptotic analysis of integro-differential systems with an unstable spectral value of the integral operator's kernel. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 67-82. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a7/