Geodesic
Dynamical inverse problem for the Lame type system (the BC-method)
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 243-268 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper, for a Lame-type system, the inverse problem on recovering the fast wave velocity from the boundary dynamical data (the response operator) is solved. The velocity is determined in the near-boundary domain, the depth of determination being proportional to the observation time. We use the BC-method, which is an approach to inverse problems based on their connections with boundary control theory. 
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     title = {Dynamical inverse problem for the {Lame} type system (the {BC-method)}},
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V. G. Fomenko. Dynamical inverse problem for the Lame type system (the BC-method). Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 243-268. http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a13/

[1] M. I. Belishev, “Dynamical inverse problem for a Lame type system”, J. Inverse and Ill-Posed Problems, 14:8 (2006), 751–766 | DOI | MR | Zbl

[2] V. G. Fomenko, “Dinamicheskaya obratnaya zadacha dlya sistemy tipa Lame (VS-metod)”, Zap. nauchn. semin. POMI, 426, 2014, 218–259

[3] M. I. Belishev, V. G. Fomenko, “O dostizhimykh mnozhestvakh dinamicheskoi sistemy tipa Lame”, Probl. mat. analiza, 70 (2013), 57–70 | Zbl

[4] V. G. Fomenko, Dinamicheskaya obratnaya zadacha dlya sistemy tipa Lame (VS-metod), Avtoref. diss. ... kand. fiz.-mat. nauk, Izd-vo Admiral, SPb, 2016, 16 pp.

[5] M. I. Belishev, A. S. Blagoveschenskii, Dinamicheskie obratnye zadachi teorii voln, Izd-vo S.-Peterburgskogo un-ta, SPb., 1999

[6] M. I. Belishev, “Granichnoe upravlenie i tomografiya rimanovykh mnogoobrazii (VS-metod)”, Uspekhi matem. nauk, 72:4 (436) (2017), 3–66 | DOI | MR | Zbl

[7] M. I. Belishev, I. Lasiecka, “The dynamical Lame system: regularity of solutions, boundary controllability and boundary data continuation”, J. ESAIM: Control, Optimisation and Calculues of Variations, 8 (2002), 143–167 | DOI | MR | Zbl

[8] M. I. Belishev, “Recent progress in the boundary control method”, Inverse Problems, 23:5 (2007), R1–R67 | DOI | MR | Zbl

[9] M. I. Belishev, “O rekonstruktsii rimanova mnogoobraziya po granichnym dannym: teoriya i plan chislennogo eksperimenta”, Zap. nauchn. semin. POMI, 380, 2010, 8–30

[10] M. I. Belishev, “Opredelenie rasstoyanii do virtualnogo istochnika po dinamicheskim granichnym dannym”, Zap. nauchn. semin. POMI, 393, 2011, 29–45

[11] M. I. Belishev, M. N. Demchenko, “Time-optimal reconstruction of Riemannian manifold via boundary electromagnetic measurements”, J. Inverse and Ill–Posed Problems, 19:2 (2011), 167–188 | DOI | MR | Zbl

[12] E. B. Bykhovskii, N. V. Smirnov, “Ob ortogonalnom razlozhenii prostranstva vektor-funktsii, kvadratichno summiruemykh po zadannoi oblasti, i operatorakh vektornogo analiza”, Tr. Matem. in-ta AN SSSR, 59, 1960, 5–36

[13] O. A. Ladyzhenskaya, Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970

[14] O. A. Ladyzhenskaya, V. A. Solonnikov, “O printsipe linearizatsii i invariantnykh mnogoobraziyakh dlya zadachi magnitogidrodinamiki”, Zap. nauchn. semin. LOMI, 38, 1973, 46–93 | Zbl

[15] V. G. Fomenko, “Operator reaktsii sistemy Lame”, Slozhnye sistemy i protsessy, 1:17 (2010), 13–18

[16] M. I. Belishev, A. K. Glasman, “Dinamicheskaya obratnaya zadacha dlya sistemy Maksvella: vosstanovlenie skorosti v regulyarnoi zone (VS-metod)”, Algebra i analiz, 12:2 (2000), 131–187 | Zbl

[17] M. Eller, V. Isakov, G. Nakamura, D. Tataru, “Uniqueness and stability in the Cauchy problem for Maxwell's and elasticity systems”, Nonlinear PDE and Applications, College de France Seminar, 14, eds. D. Cioranescu, J-L. Lions, 329–349 ; Studies in Mathematics and its applications, 31, North-Holland, Elsevier Science, 2002 | MR | MR

[18] L. Pestov, G. Uhlmann, H. Zhou, “An inverse kinematic problem with internal sources”, Inverse Problems, 31:5 (2015), 055006 | DOI | MR | Zbl

[19] M. Sh. Birman, M. Z. Solomyak, Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, LGU, L., 1980