Geodesic
``Splashes'' in Fredholm Integro-Differential Equations with Rapidly Varying Kernels
Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 163-179.

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

We consider a singularly perturbed Fredholm integro-differential equation with a rapidly varying kernel. We derive an algorithm for constructing regularized asymptotic solutions. It is shown that, given a rapidly decreasing multiplier of the kernel, the original problem does no involve the spectrum (i.e., it is solvable for any right-hand side).
Keywords: integro-differential equation, splash function, Fredholm operator, Volterra operator, regularization of an integral, boundary layer.
Mots-clés : Lagrange–Sylvester polynomial 
@article{MZM_2009_85_2_a0,
     author = {A. A. Bobodzhanov and V. F. Safonov},
     title = {``Splashes'' in {Fredholm} {Integro-Differential} {Equations} with {Rapidly} {Varying} {Kernels}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--179},
     publisher = {mathdoc},
     volume = {85},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_2_a0/}
}
TY  - JOUR
AU  - A. A. Bobodzhanov
AU  - V. F. Safonov
TI  - ``Splashes'' in Fredholm Integro-Differential Equations with Rapidly Varying Kernels
JO  - Matematičeskie zametki
PY  - 2009
SP  - 163
EP  - 179
VL  - 85
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_85_2_a0/
LA  - ru
ID  - MZM_2009_85_2_a0
ER  - 
%0 Journal Article
%A A. A. Bobodzhanov
%A V. F. Safonov
%T ``Splashes'' in Fredholm Integro-Differential Equations with Rapidly Varying Kernels
%J Matematičeskie zametki
%D 2009
%P 163-179
%V 85
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_85_2_a0/
%G ru
%F MZM_2009_85_2_a0
A. A. Bobodzhanov; V. F. Safonov. ``Splashes'' in Fredholm Integro-Differential Equations with Rapidly Varying Kernels. Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 163-179. http://geodesic.mathdoc.fr/item/MZM_2009_85_2_a0/

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

[2] B. T. Kalimbetov, V. F. Safonov, “Metod regulyarizatsii dlya sistem s nestabilnym spektralnym znacheniem yadra integralnogo operatora”, Differents. uravneniya, 31:4 (1995), 696–706 | MR | Zbl

[3] A. A. Bobodzhanov, V. F. Safonov, B. T. Kalimbetov, “Kontrastnye struktury v integrodifferentsialnykh uravneniyakh s bystro izmenyayuschimisya yadrami”, Vestn. MEI, 2002, no. 6, 15–27

[4] A. A. Bobodzhanov, V. F. Safonov, “Singulyarno vozmuschennye integrodifferentsialnye uravneniya Fredgolma s bystro izmenyayuschimisya yadrami”, Vestn. MEI, 2007, no. 6, 14–21

[5] A. A. Bobodzhanov, V. F. Safonov, “Integralnye uravneniya Volterra s bystro izmenyayuschimisya yadrami i ikh asimptoticheskoe integrirovanie”, Matem. sb., 192:8 (2001), 53–78 | MR | Zbl

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

[7] S. Yu. Dzyadyk, “O povedenii reshenii neodnorodnykh differentsialnykh uravnenii s tochkoi povorota s malym parametrom pri proizvodnoi”, Ukr. matem. zhurn., 25:5 (1973), 657–662 | MR | Zbl

[8] V. Vazov, Asimptoticheskoe razlozhenie reshenii obyknovennykh differentsialnykh uravnenii, Mir, M., 1968 | MR | Zbl