This article is cited in 1 paper

COMPUTER SCIENCE. CALCULATION EQUIPMENT. MANAGEMENT

To the question of solvability of the Cauchy problem for one loaded hyperbolic equation of the second order

A. H. Attaev

Institute of Applied Mathematics and Automation – branch of the FSBSE "Federal Scientific Center "Kabardin-Balkar Scientific Center of the Russian Academy of Sciences", 360000, KBR, Nalchik, Shortanov street, 89 A

Abstract: In this paper, the object of study is a one-dimensional loaded wave equation with a load propagating along one of its characteristics. For it, the Cauchy problem with data on one of the characteristics is posed and its unambiguous solvability is proved. It is shown, that the characteristics of this equation as Cauchy data carriers are unequal. The areas of dependence, influence and definition of initial data, which are set on the characteristic y=x, are described.

Keywords: cauchy's task, the wave equation, the loaded equation.

UDC: 517.956.3

Received: 15.12.2018

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