Geodesic
Ray method and questions of identification of the elasticity theory equations
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 1, pp. 11-27 Cet article a éte moissonné depuis la source Math-Net.Ru

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We use algebro-analytical methods to establish numerous connections in finite and infinte variants between amplitudes, coefficients, and source functions for dynamical systems of elasticity theory.
Keywords: ray method, elasticity theory equations, identification problems. 
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Yu. E. Anikonov; N. B. Ayupova; M. V. Neshchadim. Ray method and questions of identification of the elasticity theory equations. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 18 (2018) no. 1, pp. 11-27. http://geodesic.mathdoc.fr/item/VNGU_2018_18_1_a1/

[1] L. Ljung, System Identification: Theory for the User, Prentice Hall PTR, New Jersey, 1999 | MR

[2] Yu. E. Anikonov, “Constructive methods of studying the inverse problems for evolution equations”, J. Appl. Ind. Math., 3:3 (2009), 301–317 | DOI | MR

[3] Yu. E. Anikonov, M. V. Neshchadim, On Analytical Methods in the Theory of Inverse Problems of Mathematical Physics, Preprint No 234, IM SO RAN USSR, Novosibirsk, 2009 (in Russian)

[4] Yu. E. Anikonov, M. V. Neshchadim, “On analytical methods in the theory of inverse problems for hyperbolic equations. I”, J. Appl. Indust. Math., 5:4 (2011), 506–518 | DOI | MR | Zbl

[5] Yu. E. Anikonov, M. V. Neshchadim, “On analytical methods in the theory of inverse problems for hyperbolic equations. II”, J. Appl. Indust. Math., 6:1 (2012), 6–11 | DOI | MR

[6] Yu. E. Anikonov, M. V. Neshchadim, “Analytical methods of the theory of inverse problems for parabolic equations”, J. Math. Sci., 195:6 (2013), 754–770 | DOI | MR

[7] Yu. E. Anikonov, “Representations of solutions to functional and evolution equations and identification problems”, Siberian Electronic Mathematical Reports, 10 (2013), 591–614 (in Russian) | MR | Zbl

[8] Yu. E. Anikonov, N. B. Ayupova, “The Hopf-Cole transformation and multidimensional representation of solutions to evolution equations”, J. Appl. Indust. Math., 9:1 (2015), 11–17 | DOI | MR | Zbl

[9] Yu. E. Anikonov, N. B. Ayupova, V. G. Bardakov, V. P. Golubyatnikov, “Inversion of mapping and inverse problems”, Siberian Electronic Mathematical Reports, 9 (2012), 382–432 (in Russian) | Zbl

[10] Yu. E. Anikonov, M. V. Neshchadim, “The method of differential constraints and nonlinear inverse problems”, J. Appl. Indust. Math., 9:3 (2015), 317–327 | DOI | MR | Zbl

[11] Yu. E. Anikonov, M. V. Neshchadim, “Algebraic-analytic methods for constructing solutions to differential equations and inverse problems”, J. Math. Sci., 215:6 (2016), 444–459 | DOI | MR

[12] V. M. Babich, V. S. Buldyrev, Asymptotic Methods in Short Wave Diffraction Problems, 1972, Nauka, M. (in Russian)

[13] V. M. Babich, V. S. Buldyrev, I. A. Molotkov, Space-time Ray Method, Leningrad State University Press, Leningrad, 1985 (in Russian)

[14] V. M. Babich, A. P. Kiselev, Elastic Waves: High Frequency Theory, BHV-Petersburg, Saint-Petersburg, 2014 (in Russian)

[15] Podilchuk Yu. N., Rubtsov Yu. K., Luchevye metody v teorii rasprostraneniya i rasseyaniya voln, Nauk. dum., Kiev, 1988

[16] Rossikhin Yu. A., Shitikova M. V., “Ray Method for Solving Dynamic Problems Connected with Propagation of Wave Surfaces of Strong and Weak Discontinuities”, Appl. Mech. Rev., 48:1 (1995), 1–39 | DOI | MR

[17] Yu. E. Anikonov, N. B. Ayupova, “Ray splittings and identities for the second-order equations with applications to inverse problems”, Sib. J. of Pure and App. Math., 17:1 (2017), 3–16 (in Russian)

[18] M. V. Neshchadim, “Functionally invariant solutions to maxwell's system”, J. Appl. Ind. Math., 11:1 (2017), 107–114 | DOI | MR | Zbl

[19] L. I. Sedov, Mechanics of Continuous Media, v. 1, 2,, Series in Theoretical and Applied Mechanics, 4, World Scientific Publishing Co., Inc., River Edge, NJ, 1997 | MR | Zbl

[20] A. G. Kulikovskii, E. I. Sveshnikova, Nonlinear Waves in Elastic Media, CRC Press, New York, 1995 | MR | Zbl