We develop a new method for studying inverse problems of mathematical physics by using systems of equations of ray expansion of solutions to parabolic and hyperbolic equations with variable coefficients.
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Yu. E. Anikonov, “Constructive methods of studying the inverse problems for evolution equations,” J. Appl. Indust. Math. 3, No. 3, 301–317 (2009).
Yu. E. Anikonov and M. V. Neshchadim, “On analytical methods in the theory of inverse problems for hyperbolic equations. I,” J. Appl. Ind. Math. 5, No. 4, 506–518 (2011).
Yu. E. Anikonov and M. V. Neshchadim, “On analytical methods in the theory of inverse problems for hyperbolic equations. II,” J. Appl. Ind. Math. 6, No. 1, 6–11 (2012).
Yu. E. Anikonov and M. V. Neshchadim, “Analytical methods of the theory of inverse problems for parabolic equations,” J. Math. Sci., New York 195, No. 6, 754–770 (2013).
Yu. E. Anikonov, “Representation of solutions to functional and evolution equations and identification problems,” Sib. Èlektron. Mat. Izv. 10, 591–614, electronic only (2013).
Yu. E. Anikonov, “Differential identities for partial differential equations” [in Russian], Sib. Zh. Ind. Mat., 17, No. 2, 11–17 (2014).
Yu. E. Anikonov and N. B. Ayupova, “The Hopf-Cole transformation and multidimensional representation of solutions to evolution equations,” J. Appl. Indust. Math. 9, No. 1, 11–17 (2015).
Yu. E. Anikonov and M. V. Neshchadim, “Differential identities for nonlinear partial differential equations,” J. Math. Sci., New York 215, No. 4, 436–443 (2016).
Yu. E. Anikonov and M. V. Neshchadim, “The method of differential constraints and nonlinear inverse problems,” J. Appl. Indust. Math. 9, No. 3, 317–327 (2015).
Yu. E. Anikonov and M. V. Neshchadim, “Algebraic-analytic methods for constructing solutions to differential equations and inverse problems,” J. Math. Sci., New York 215, No. 4, 444–459 (2016).
Yu. E. Anikonov, N. B. Ayupova, V. G. Bardakov, V. P. Golubyatnikov, and M. V. Neshchadim, “Inversion of mapping and inverse problems” [in Russian], Sib. Èlektron. Mat. Izv. 9, 382–432, electronic only (2012).
V. S. Vladimirov, Equations of Mathematical Physics, Marcel Dekker, New York (1971).
V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of Diffraction of Short Waves, [in Russian], Nauka, Moscow (1972).
B. A. Dubrovin, A. T. Fomenko, and S. P. Novikov, Modern Geometry – Methods and Applications, Springer, New York etc. I (1984); II (1985); III (1990).
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Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 17, No. 1, 2017, pp. 3-16.
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Anikonov, Y.E., Ayupova, N.B. Ray Expansions and Identities for Second Order Equations. Applications to Inverse Problems. J Math Sci 231, 111–123 (2018). https://doi.org/10.1007/s10958-018-3809-x
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DOI: https://doi.org/10.1007/s10958-018-3809-x