This article is cited in 1 paper

Differential Equations and Mathematical Physics

The Cauchy problem for a general hyperbolic differential equation of the $n$-th order with the nonmultiple characteristics

A. A. Andreev^a, J. O. Yakovleva<sup>b

a</sup> Samara State Technical University, Samara, 443100, Russian Federation
^b Samara National Research University, Samara, 443086, Russian Federation

Abstract: In the paper the problem of Cauchy is considered for the hyperbolic differential equation of the $n$-th order with the nonmultiple characteristics. The Cauchy problem is considered for the hyperbolic differential equation of the third order with the nonmultiple characteristics for example. The analogue of D'Alembert formula is obtained as a solution of the Cauchy problem for the hyperbolic differential equation of the third order with the nonmultiple characteristics. The regular solution of the Cauchy problem for the hyperbolic differential equation of the forth order with the nonmultiple characteristics is constructed in an explicit form. The regular solution of the Cauchy problem for the $n$-th order hyperbolic differential equation with the nonmultiple characteristics is constructed in an explicit form. The analogue of D'Alembert formula is obtained as a solution of this problem also. The existence and uniqueness theorem for the regular solution of the Cauchy problem for the $n$-th order hyperbolic differential equation with the nonmultiple characteristics is formulated as the result of the research.

Keywords: $n$-th order hyperbolic differential equation, nonmultiple characteristics, Cauchy problem, D'Alembert formula.

UDC: 517.956.3

MSC: 35L25

Original article submitted 10/IV/2016
revision submitted – 21/V/2016

DOI: 10.14498/vsgtu1490

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