This article is cited in 6 papers

Short Communication

The Cauchy problem for a system of the hyperbolic differential equations 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 Cauchy problem is considered for the hyperbolic differential equation of the $n$-th order with the nonmultiple characteristics. The regular solution of the Cauchy problem for the hyperbolic differential equation of the $n$-th order with the nonmultiple characteristics is considered. In the paper the solution of the Cauchy problem for the system of the hyperbolic differential equations of the $n$-th order with the nonmultiple characteristics is considered. The existence and uniqueness theorem for the regular solution of the Cauchy problem for the system of the hyperbolic differential equations of the $n$-th order with the nonmultiple characteristics is considered as the result of the research.

Keywords: $n$-th order hyperbolic differential equation, system of the hyperbolic differential equations of the $n$-th order, nonmultiple characteristics, method of the general solutions, Cauchy problem, D'Alembert formula.

UDC: 517.956.3

MSC: 35L56

Received: November 17, 2017
Revised: December 13, 2017
Accepted: December 18, 2017
First online: December 25, 2017

DOI: 10.14498/vsgtu1577

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