Geodesic
Regularized asymptotic solutions of integrodifferential equations with a zero operator of differential part and with several quickly varying kernels
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1566-1575

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

The paper considers an integro-differential equation with the zero operator of the differential part and with several quickly changing integral kernels. The work is a continuation of the authors’ research, carried out earlier for one quickly changing integral kernel. The main ideas of such a generalization and subtleties arising in the development of the algorithm of the Lomov regularization method are fully visible in the case of two quickly changing integral kernels. After constructing an equivalent integro-differential system and its regularization, the theory of normal and unique solvability of the corresponding iterative problems is developed, which is the basis of the algorithm for constructing asymptotic solutions of the original problem.
Keywords: singularly perturbed, integro-differential equations, regularization of the integral. 
@article{SEMR_2018_15_a142,
     author = {M. A. Bobojanova and V. F. Safonov},
     title = {Regularized asymptotic solutions of integrodifferential equations with a zero operator of differential part and with several quickly  varying kernels},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1566--1575},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a142/}
}
TY  - JOUR
AU  - M. A. Bobojanova
AU  - V. F. Safonov
TI  - Regularized asymptotic solutions of integrodifferential equations with a zero operator of differential part and with several quickly  varying kernels
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 1566
EP  - 1575
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a142/
LA  - ru
ID  - SEMR_2018_15_a142
ER  - 
%0 Journal Article
%A M. A. Bobojanova
%A V. F. Safonov
%T Regularized asymptotic solutions of integrodifferential equations with a zero operator of differential part and with several quickly  varying kernels
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 1566-1575
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a142/
%G ru
%F SEMR_2018_15_a142
M. A. Bobojanova; V. F. Safonov. Regularized asymptotic solutions of integrodifferential equations with a zero operator of differential part and with several quickly  varying kernels. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1566-1575. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a142/