Some representations of solutions to Blokhintsev equation
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1697-1709.

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In the paper, we obtain some representations for solutions and coefficients of Blokhintsev equation under condition the solutions satisfy to supplementary quasi-linear equation. These results may be used in the problems of identification of solutions and coefficients given supplementary initial-boundary information.
Keywords: method of differential constrains,overdetermined systems of partial differential equations.
Mots-clés : Blokhintsev equation
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Yu. E. Anikonov; N. B. Ayupova; M. V. Neshchadim. Some representations of solutions to Blokhintsev equation. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1697-1709. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a101/

[1] D.I. Blokhintsev, Acoustics of a nonhomogeneous moving medium, NACA Tech. Memo., Washington, 1956 | MR

[2] A.F. Sidorov, V.P. Shapeev, N.N. Yanenko, Method of differential relations and its applications in gas dynamics, Nauka, Novosibirsk, 1984 | MR | Zbl

[3] Yu.E. Anikonov, N.B. Ayupova, “Remarks on identification theory”, Sib. Elektron. Mat. Izv., 15 (2018), 1091–1102 | MR | Zbl

[4] S.P. Finikov, Cartan's method of exterior forms in differential geometry, Gostechizdat, M.-L., 1948 | Zbl

[5] J.-F. Pommaret, Systems of partial differential equations and Lie pseudogroups, Gordon and Breach, New York etc, 1978 | MR | Zbl

[6] L.V. Ovsyannikov, Group analysis of differential equations, Academic Press, New York etc, 1982 | MR | Zbl

[7] V.I. Smirnov, S.L. Sobolev, On new method of solution to plane problem of elastique vibrations, Trudy Seism. Inst. AN SSSR, 20, 1932

[8] V.I. Smirnov, S.L. Sobolev, On application of new method to study of elastique vibrations in space involving axiality, Trudy Seism. Inst. AN SSSR, 29, 1933

[9] N.P. Erugin, M.M. Smirnov, “Functionally invariant solutions of differential equations”, Differ. Equ., 17:5 (1981), 563–573 | MR | Zbl

[10] A.P. Kiselev, M.V. Perel', “Relatively distortion-free waves for the m-dimensional wave equation”, Differ. Equ., 38:8 (2002), 1206–1207 | DOI | MR | Zbl

[11] M.V. Neshchadim, “Solutions to the system of Maxwell equations with invariants equal to zero”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 6:3 (2006), 59–61 | MR | Zbl

[12] M.S. Shneerson, “Maxwell's equations and functionally invariant solutions of the wave equation”, Differ. Uravn., 4:4 (1968), 743–758 | MR | Zbl

[13] C.B. Collins, “Complex potential equations. I: A technique for solutions”, Math. Proc. Cambr. Phil. Soc., 80:1 (1976), 165–171 | DOI | MR | Zbl

[14] F.G. Friedlander, “Simple progressing solutions of the wave equation”, Proc. Camb. Phil. Soc., 43:3 (1947), 360–373 | DOI | MR | Zbl

[15] A.P. Kiselev, M.V. Perel, “Highly localized solutions of the wave equation”, J. Math. Phys., 41:4 (2000), 1934–1955 | DOI | MR | Zbl

[16] P.K. Rashevskii, The Geometric Theory of Partial Differential Equations, OGIZ, M.-L., 1947 | MR | Zbl

[17] M.V. Neshchadim, “Classes of generalized functional invariant solutions of wave equation. I”, Sib. Electron. Mat. Izv., 10 (2013), 418–435 | MR | Zbl

[18] Yu.E. Anikonov, M.V. Neshchadim, “Representations for the solutions and coefficients of second-order differential equations”, J. Appl. Ind. Math., 7:1 (2013), 15–21 | DOI | MR | Zbl

[19] Yu.E. Anikonov, M.V. Neshchadim, “Representations for the solutions and coefficients of evolution equations”, J. Appl. Ind. Math., 7:3 (2013), 326–334 | DOI | MR | Zbl