Geodesic
Volterra integral equations with rapidly varying kernels and their asymptotic integration
Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1139-1164 
A. A. Bobodzhanov; V. F. Safonov. Volterra integral equations with rapidly varying kernels and their asymptotic integration. Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1139-1164. http://geodesic.mathdoc.fr/item/SM_2001_192_8_a2/
@article{SM_2001_192_8_a2,
     author = {A. A. Bobodzhanov and V. F. Safonov},
     title = {Volterra integral equations with rapidly varying kernels and their asymptotic integration},
     journal = {Sbornik. Mathematics},
     pages = {1139--1164},
     year = {2001},
     volume = {192},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_8_a2/}
}
TY  - JOUR
AU  - A. A. Bobodzhanov
AU  - V. F. Safonov
TI  - Volterra integral equations with rapidly varying kernels and their asymptotic integration
JO  - Sbornik. Mathematics
PY  - 2001
SP  - 1139
EP  - 1164
VL  - 192
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_2001_192_8_a2/
LA  - en
ID  - SM_2001_192_8_a2
ER  - 
%0 Journal Article
%A A. A. Bobodzhanov
%A V. F. Safonov
%T Volterra integral equations with rapidly varying kernels and their asymptotic integration
%J Sbornik. Mathematics
%D 2001
%P 1139-1164
%V 192
%N 8
%U http://geodesic.mathdoc.fr/item/SM_2001_192_8_a2/
%G en
%F SM_2001_192_8_a2

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

This paper is concerned with a singularly perturbed integral system with rapidly varying kernels. In contrast to integral equations with slowly varying kernels, where regularization is carried out with respect to the spectrum of the “diagonal” kernel, the regularization problem in the case of rapidly varying kernels is solved in terms of the spectrum of a certain extended operator. The goal here is to construct this operator and develop an appropriate algorithm for asymptotic solutions.

[1] Imanaliev M. I., Metody resheniya nelineinykh obratnykh zadach i ikh prilozhenie, Ilim, Frunze, 1977 | MR | Zbl

[2] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya reshenii singulyarno vozmuschennykh uravnenii, Nauka, M., 1973 | MR | Zbl

[3] Lomov S. A., Vvedenie v obschuyu teoriyu singulyarnykh vozmuschenii, Nauka, M., 1981 | MR

[4] Lomov S. A., Introduction to the general theory of singular perturbations, Amer. Math. Soc., Providence, RI, 1992 | MR | Zbl

[5] Safonov V. F., Tuichiev O. D., “Regulyarizatsiya singulyarno vozmuschennykh integralnykh uravnenii s bystro izmenyayuschimisya yadrami i ikh asimptotika”, Differents. uravneniya, 33:9 (1997), 1199–1211 | MR

[6] Gantmakher F. R., Teoriya matrits, GITTL, M., 1953

[7] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl