Geodesic
The problem of finding the kernels in the system
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 2, pp. 38-61

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

We pose the direct and inverse problem of finding the electromagnetic field and the diagonal memory matrix for the reduced canonical system of integro-differential Maxwell's equations. The problems are replaced by a closed system of Volterra-type integral equations of the second kind with respect to the Fourier transform in the variables $x_1$ and $x_2$ of the solution to the direct problem and the unknowns of the inverse problem. To this system, we then apply the method of contraction mapping in the space of continuous functions with a weighted norm. Thus, we prove the global existence and uniqueness theorems for solutions to the posed problems.
Keywords: hyperbolic system, system of Maxwell's equations, integral equation, contraction mapping principle. 
@article{SJIM_2021_24_2_a2,
     author = {D. K. Durdiev and K. K. Turdiev},
     title = {The problem of finding the kernels in the system},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {38--61},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2021_24_2_a2/}
}
TY  - JOUR
AU  - D. K. Durdiev
AU  - K. K. Turdiev
TI  - The problem of finding the kernels in the system
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2021
SP  - 38
EP  - 61
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2021_24_2_a2/
LA  - ru
ID  - SJIM_2021_24_2_a2
ER  - 
%0 Journal Article
%A D. K. Durdiev
%A K. K. Turdiev
%T The problem of finding the kernels in the system
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2021
%P 38-61
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2021_24_2_a2/
%G ru
%F SJIM_2021_24_2_a2
D. K. Durdiev; K. K. Turdiev. The problem of finding the kernels in the system. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 2, pp. 38-61. http://geodesic.mathdoc.fr/item/SJIM_2021_24_2_a2/