Geodesic
Determination of a non-stationary adsorption coefficient analytical in part of spatial variables
Matematičeskie trudy, Tome 25 (2022) no. 2, pp. 88-106.

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The multidimensional adsorption coefficient inverse problem is considered for a second order hyperbolic equation. It is supposed that this coefficient is continuous with respect to the variables $t$, $x$ and analytic in the other spatial variables. For solving this equation, the scale method of Banach spaces of analytic functions is applied. The problem are reduced to a system of nonlinear Volterra integral equations and the local existence, global uniqueness, stability estimates are established. 
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D. K. Durdiev; Zh. D. Totieva. Determination of a non-stationary adsorption coefficient analytical in part of spatial variables. Matematičeskie trudy, Tome 25 (2022) no. 2, pp. 88-106. http://geodesic.mathdoc.fr/item/MT_2022_25_2_a2/

[1] Romanov V. G., Ustoichivost v obratnykh zadachakh, Nauchnyi mir, M., 2005 | MR

[2] Ovsyannikov L. V., “Singulyarnyi operator v shkale banakhovykh prostranstv”, Dokl. AN SSSR, 6:4 (1965), 1025–1028 | Zbl

[3] Ovsyannikov L. V., “Nelineinaya zadacha Koshi v shkale banakhovykh prostranstv”, Dokl. AN SSSR, 200:4 (1971), 789–792 | Zbl

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

[5] Romanov V. G., “O lokalnoi razreshimosti nekotorykh mnogomernykh obratnykh zadach dlya uravnenii giperbolicheskogo tipa”, Differents. uravneniya, 25:2 (1989), 203–209 | MR | Zbl

[6] Romanov V. G., “O razreshimosti obratnykh zadach v klasse funktsii, analiticheskikh po chasti peremennykh”, Dokl. AN SSSR, 304:4 (1989), 807–811 | MR | Zbl

[7] Durdiev D. K. and Nuriddinov Z. Z., “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

[8] Bozorov Z. R., “Zadacha opredeleniya dvumernogo yadra uravneniya vyazkouprugosti”, Sib. zhurn. industr. matematiki, 23:1 (2020), 28–45 | MR | Zbl

[9] Durdiev D. K., Rakhmonov A. A., “Zadacha ob opredelenii dvumernogo yadra v sisteme integro-differentsialnykh uravnenii vyazkouprugoi poristoi sredy”, Sib. zhurn. industr. matematiki, 23:2 (2020), 63–80 | Zbl

[10] Durdiev D. K., Totieva Zh. D., “Zadacha opredeleniya mnogomernogo yadra uravneniya vyazkouprugosti”, Vladikavk. matem. zhurn., 17:4 (2015), 18–43 | MR | Zbl

[11] Durdiev D. K., Safarov Zh. Sh., “Lokalnaya razreshimost zadachi opredeleniya prostranstvennoi chasti mnogomernogo yadra v integro-differentsialnom uravnenii giperbolicheskogo tipa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 29:4 (2012), 37–47 | DOI | Zbl

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

[13] Kabanikhin S. I., Satybaev A. D., Shishlenin M. A., Direct methods of solving inverse multidimensional hyperbolic problems, VSP, Utrecht, 2005 | MR | Zbl

[14] Romanov V. G., “Ustoichivost v obratnykh zadachakh dlya giperbolicheskikh uravnenii”, Sib. elektron. matem. izv., 7:1 (2010), 4–10 | MR

[15] Kabanikhin S. I., Shishlenin M. A., “Ob ispolzovanii apriornoi informatsii v koeffitsientnykh obratnykh zadachakh dlya giperbolicheskikh uravnenii”, Tr. IMM UrO RAN, 18, no. 1, 2012, 147–164

[16] Romanov V. G., “A problem of recovering a special two dimension potential in a hyperbolic equation”, Eurasian Journal of Mathematical and Computer Applications, 4:1 (2016), 32–46 | DOI

[17] Denisov A. M., “Suschestvovanie resheniya obratnoi koeffitsientnoi zadachi dlya kvazilineinogo giperbolicheskogo uravneniya”, Zh. vychisl. matem. i matem. fiz., 59:4 (2019), 587–596 | DOI | MR | Zbl