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Representation of Solutions to Equations of Hyperbolic Type / Ulukhanyan A.R. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 2. P. 62-66 [Moscow Univ. Mech. Bulletin. Vol. 65, No 2, 2010. P. 47-50]. The general solutions to hyperbolic equations of fourth and sixth order are obtained using Vekua's method for the representation of the general solutions to elliptic equations of order 2n with the aid of n analytic functions. It is assumed that the right-hand sides of the hyperbolic equations can be expanded in time series of sines. The systems of equations of various approximations for a prismatic thin body in terms of moments with respect to the system of Legendre polynomials can be reduced to these equations and to some hyperbolic-type equations of higher order.
Key words: thin body, moments of functions with respect to a system of Legendre
polynomials, general solution, hyperbolic-type equations, elliptic-type
equations, analytic functions, orthogonal polynomials.
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