Geodesic
Determination of non-stationary potential analytical with respect to spatial variables
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 565-576

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

The inverse problem of determining coefficient before the lower term of the hyperbolic equation of the second order is considered. The coefficient depends on time and $n$ spatial variables. It is supposed that this coefficient is continuous with respect to variables $t, x$ and it is analytic in other spatial variables. The problem is reduced to the equivalent integro-differential equations with respect to unknown functions. To solve this equations the scale method of Banach spaces of analytic functions is applied. The local existence and global uniqueness results are proven. The stability estimate is also obtained.
Keywords: inverse problem, Cauchy problem, fundamental solution, local solvability, Banach space. 
@article{JSFU_2022_15_5_a2,
     author = {Durdimurod K. Durdiev and Zhanna D. Totieva},
     title = {Determination of non-stationary potential analytical with respect to spatial variables},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {565--576},
     publisher = {mathdoc},
     volume = {15},
     number = {5},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a2/}
}
TY  - JOUR
AU  - Durdimurod K. Durdiev
AU  - Zhanna D. Totieva
TI  - Determination of non-stationary potential analytical with respect to spatial variables
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2022
SP  - 565
EP  - 576
VL  - 15
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a2/
LA  - en
ID  - JSFU_2022_15_5_a2
ER  - 
%0 Journal Article
%A Durdimurod K. Durdiev
%A Zhanna D. Totieva
%T Determination of non-stationary potential analytical with respect to spatial variables
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2022
%P 565-576
%V 15
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a2/
%G en
%F JSFU_2022_15_5_a2
Durdimurod K. Durdiev; Zhanna D. Totieva. Determination of non-stationary potential analytical with respect to spatial variables. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 565-576. http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a2/