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/

[1] L.V. Ovsyannikov, “A singular operator in a scale of Banach spaces”, Soviet Math. Dokl., 6:4 (1965), 1025–1028 (in Russian) | MR | Zbl

[2] L.V. Ovsyannikov, “A nonlocal Cauchy problem in scales of Banach spaces”, Dokl. Akad. Nauk SSSR, 200:4 (1971), 789–792 (in Russian) | MR | Zbl

[3] L. Nirenberg, Topics in Nonlinear Functional Analysis, Courant Institute Math. Sci., New York Univ., New York, 1974 | MR | Zbl

[4] V.G. Romanov, Stability in Inverse Problems, Nauchnyi Mir, M., 2005 (in Russian) | MR | Zbl

[5] V.G. Romanov, “Local solvability of some multidimensional inverse problems for hyperbolic equations”, Differ. Equ., 25:2 (1989), 203–209 | MR | Zbl

[6] V.G. Romanov, “On solvability of inverse problems for hyperbolic equations in a class of functions analytic in part of variables”, Dokl. Akad. Nauk SSSR, 304:4 (1989), 807–811 | MR | Zbl

[7] D.K. Durdiev, Z.Z. Nuriddinov, “Determination of a multidimensional kernel in some parabolic integro–differential equation”, Journal of Siberian Federal University-Mathematics and Physics, 14:1 (2021), 117–127 | DOI | MR | Zbl

[8] Z.R. Bozorov, “The problem of determining the two-dimensional kernel of a viscoelasticity equation”, Sib. Zh. Ind. Mat., 23:1 (2020), 28–45 | DOI | MR

[9] D.K. Durdiev, A.A. Rahmonov, “The problem of determining the 2D kernel in a system of integro-differential equations of a viscoelastic porous medium”, J. Appl. Indust. Math., 14:2 (2020), 281–295 | DOI | MR

[10] D.K. Durdiev, Zh.D. Totieva, “The problem of determining the multidimensional kernel of the viscoelasticity equation”, Vladikavkaz. Mat. Zh., 17:4 (2015), 18–43 (in Russian) | MR | Zbl

[11] D.K. Durdiev, Zh.Sh. Safarov, “Local solvability of the problem of definition of the spatial part of the multidimensional kernel in an integro-differential equation of hyperbolic type”, Vestnik Samarsk. Gos. Univ. Ser. Fiz.-Mat. Nauki, 29:4 (2012), 37–47 (in Russian) | DOI | MR | Zbl

[12] D.K. Durdiev, “Some multidimensional inverse problems of memory determination in hyperbolic equations”, Zh. Mat. Fiz., Anal. Geom., 3:4 (2007), 411–423 | MR | Zbl

[13] D.K. Durdiev, “A multidimensional inverse problem for an equation with memory”, Sib. Math. J., 35:3 (1994), 514–521 (in Russian) | DOI | MR