Ray expansions and identities for the second order equations with applications to inverse problems
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 1, pp. 3-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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We develop a new method of investigation of inverse problems of mathematical physics which is based on the systems of equations of ray expansion of solutions to parabolic and hyperbolic equations with variable coefficients.
Keywords: ray expansion, inverse problems, particular solution, hyperbolic equations.
Mots-clés : parabolic equations
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Yu. E. Anikonov; N. B. Ayupova. Ray expansions and identities for the second order equations with applications to inverse problems. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 17 (2017) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/VNGU_2017_17_1_a0/

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

[2] Yu. E. Anikonov, M. V. Neshchadim, On analytical methods in the theory of inverse problems of mathematical physics, Preprint No 234, IM SO AN USSR, Novosibirsk, 2009 (in Russian) | MR

[3] 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 | MR | Zbl

[4] 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 | Zbl

[5] 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

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

[7] Yu. E. Anikonov, “Differential identities for partial differential equations”, Sib. Zh. Ind. Mat., 17:2 (2014), 11–17 (in Russian)

[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, M. V. Neshchadim, “Differential identities for nonlinear partial differential equations”, J. Math. Sci., 215:6 (2016), 436–443 | DOI | MR | MR | 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 | MR | Zbl

[12] 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) | MR | Zbl

[13] V. S. Vladimirov, Equations of Mathematical Physics, Mir Publishers, M., 1983 (in Russian) | MR

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

[15] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya, Nauka, M., 1979 ; B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry. Methods and Applications, v. 1, Graduate Texts in Mathematics, 93, Springer–Verlag, 1984 ; Modern Geometry. Methods and Applications, v. 2, Graduate Texts in Mathematics, 104, Springer–Verlag, 1985 ; Modern Geometry. Methods and Applications, v. 3, Graduate Texts in Mathematics, 124, Springer–Verlag, 1990 | MR | DOI | MR | Zbl | DOI | Zbl | DOI | Zbl