Asymptotic expansions of solutions to inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 744-752 Cet article a éte moissonné depuis la source Math-Net.Ru

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Two inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative are considered. The existence and uniqueness of their solutions are proved. As the small parameter tends to zero, the solutions of the inverse problems are proved to converge to solutions of inverse problems for a parabolic equation.
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A. M. Denisov. Asymptotic expansions of solutions to inverse problems for a hyperbolic equation with a small parameter multiplying the highest derivative. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 744-752. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a5/

[1] Lavrentev M. M., Romanov V. G., Shishatskii S. P., Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka Sib. otd-nie, Novosibirsk, 1980 | MR

[2] Romanov V. G., Obratnye zadachi matematicheskoi fiziki, Nauka, M., 1984 | MR

[3] Denisov A. M., Vvedenie v teoriyu obratnykh zadach, MGU, M., 1994

[4] Isakov V., Inverse problems for partial differential equations, Springer, New York, 1998 | MR | Zbl

[5] Prilepko A. I., Orlovsky D. G., Vasin I. A., Methods for solving inverse problems in mathematical physics, Marcel Dekker, New York, 2000 | MR | Zbl

[6] Kabanikhin S. I., Obratnye i nekorrektnye zadachi, Sib. nauch. izd-vo, Novosibirsk, 2008 | Zbl

[7] Lattes R., Lions J.-L., Methode de quasi reversibilite et applications, Dunod, Paris, 1967 | MR

[8] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, Nauka, M., 1965 | MR