Geodesic
The problem of determining the multidimensional kernel of viscoelasticity equation
Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 4, pp. 18-43 Cet article a éte moissonné depuis la source Math-Net.Ru

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The integro-differential system of viscoelasticity equations is considered. The direct problem of determining of the displacements vector from the initial-boundary problem for this system is formulated. It is assumed that the kernel in the integral part depends on both the time and the space variable $x_2$. For its determination an additional condition relative to the first component of the displacements vector with $x_3=0$ is posed. The inverse problem is replaced by the equivalent system of integral equations. The study is based on the method of scales of Banach spaces of analytic functions. The theorem on local unique solvability of the inverse problem is proved in the class of functions analytic on the variable $x_2$ and continuous on $t$. 
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D. Q. Durdiev; Zh. D. Totieva. The problem of determining the multidimensional kernel of viscoelasticity equation. Vladikavkazskij matematičeskij žurnal, Tome 17 (2015) no. 4, pp. 18-43. http://geodesic.mathdoc.fr/item/VMJ_2015_17_4_a2/

[1] Tuaeva Zh. D., “Mnogomernaya matematicheskaya model seismiki s pamyatyu”, Issledovaniya po dif. uravneniyam i mat. modelirovaniyu, Itogi nauki. YuFO. Mat. forum, 1, ch. 2, VNTs RAN, Vladikavkaz, 2008, 297–306

[2] Durdiev D. K., Totieva Zh. D., “Zadacha ob opredelenii odnomernogo yadra uravneniya vyazkouprugosti”, Sib. zhurn. industr. matem., 16:2 (2013), 72–82 | MR | Zbl

[3] Ovsyannikov L. V., “Singulyarnyi operator v shkale banakhovykh prostranstv”, Dokl. AN SSSR, 163:4 (1965), 819–822 | MR | Zbl

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

[5] Nirenberg L., Topics in Nonlinear Functional Analysis, Courant Institute Math. Sci., New York Univ., N.Y., 1974, 259 pp. | MR | Zbl

[6] Romanov V. G., “O lokalnoi razreshimosti nekotorykh mnogomernykh obratnykh zadach dlya uravnenii giperbolicheskogo tipa”, Dif. uravneniya, 25:2 (1989), 275–284 | MR

[7] Romanov V. G., “Voprosy korrektnosti zadachi opredeleniya skorosti zvuka”, Sib. mat. zhurn., 30:4 (1989), 125–134 | MR | Zbl

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

[9] Durdiev D. K., “Mnogomernaya obratnaya zadacha dlya uravneniya s pamyatyu”, Sib. mat. zhurn., 35:3 (1994), 574–582 | MR | Zbl

[10] 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

[11] Durdiev D. K., Safarov Zh. Sh., “Lokalnaya razreshimost zadachi opredeleniya prostranstvennoi chasti mnogomernogo yadra v integrodifferentsialnom uravnenii giperbolicheskogo tipa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2012, no. 4(29), 37–47 | DOI