Geodesic
Boundary-value problem for systems of convolutional equations in anisotropic functional spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Tome 182 (2020), pp. 66-69.

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

In this paper, anisotropic classes of well-posed Cauchy problems and boundary-value problems for systems of convolutions equations are obtained. For a particular case of differential equations, a hypersurface of conjugate orders of the corresponding polynomial is used, and various classes of well-posed problems are obtained.
Mots-clés : convolution equation, Fourier transform
Keywords: boundary-value problem, hypersurface of conjugate orders, anisotropic space of functions. 
@article{INTO_2020_182_a10,
     author = {{\CYRA}. {\CYRA}. Makarov},
     title = {Boundary-value problem for systems of convolutional equations in anisotropic functional spaces},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {66--69},
     publisher = {mathdoc},
     volume = {182},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_182_a10/}
}
TY  - JOUR
AU  - А. А. Makarov
TI  - Boundary-value problem for systems of convolutional equations in anisotropic functional spaces
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 66
EP  - 69
VL  - 182
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_182_a10/
LA  - ru
ID  - INTO_2020_182_a10
ER  - 
%0 Journal Article
%A А. А. Makarov
%T Boundary-value problem for systems of convolutional equations in anisotropic functional spaces
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 66-69
%V 182
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_182_a10/
%G ru
%F INTO_2020_182_a10
А. А. Makarov. Boundary-value problem for systems of convolutional equations in anisotropic functional spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 4, Tome 182 (2020), pp. 66-69. http://geodesic.mathdoc.fr/item/INTO_2020_182_a10/

[1] Volevich L. R., Gindikin S. G., “Zadacha Koshi i svyazannye s nei zadachi dlya uravnenii tipa svertki”, Usp. mat. nauk., 27:4 (166) (1972), 65-–143 | MR | Zbl

[2] Volevich L. R., Gindikin S. G., Obobschennye funktsii i uravneniya v svertkakh, Fizmatlit, M., 1994 | MR

[3] Makarov A. A., “Kriterii korrektnoi razreshimosti kraevoi zadachi v sloe dlya sistemy lineinykh uravnenii v svertkakh v topologicheskikh prostranstvakh”, Teoreticheskie i prikladnye voprosy differentsialnykh uravnenii i algebry, Naukova dumka, Kiev, 1978, 178–180

[4] Makarov A. A., “O neobkhodimykh i dostatochnykh usloviyakh korrektnoi razreshimosti kraevoi zadachi v sloe dlya sistem differentsialnykh uravnenii v chastnykh proizvodnykh”, Differ. uravn., 17:2 (1981), 320–324 | MR | Zbl

[5] Serdyuk G. P., O edinstvennosti reshenii lineinykh differentsialnykh uravnenii, Diss. na soisk. uch. step. kand. fiz.-mat. nauk, KhGU, Kharkov, 1983