This article is cited in 1 paper

Short Communication
Differential Equations

A Mixed Problem for One 3D Space Analogue of Hyperbolic Type Equation

M. V. Dolgopolov^a, I. N. Rodionova<sup>b

a</sup> Dept. of General and Theoretical Physics, Scientific Research Laboratory of Mathematical Physics, Samara State University, Samara
^b Dept. of Mathematics and Business Informatic, Samara State University, Samara

Abstract: It is well known that differential equations with an operator are used for study of the processes connected with appearances of vibration and other mechanics problems, and also play an essential role in the theory of approximation and mapping. In the present work a unique solution for the mixed problem of the full hyperbolic equation of the third order with constant factors, in a three-dimensional Euclidean space, was obtain with the Riemann method, which then becomes considerably simpler at the expense of integral representation of one of boundary conditions. Owing to this it can be used for statement and a solution of new boundary value problems.

Keywords: integral equations, boundary value problems, hyperbolic type equations.

UDC: 517.956.3

MSC: 35L25, 35L35

Original article submitted 03/IX/2010
revision submitted – 29/IX/2010

DOI: 10.14498/vsgtu828

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