This article is cited in 3 papers

Short Communication

The Goursat-type problem for a hyperbolic equation and system of third order hyperbolic equations

A. A. Andreev, J. O. Yakovleva

Samara State Technical University, Samara, 443100, Russian Federation

Abstract: In the first part of this study, the well-posed Goursat-type problem is considered for the hyperbolic differential equation of the third order with non-multiple characteristics. The example illustrating the non-well-posed Goursat-type problem for the hyperbolic differential equation of the third order is discussed. The regular solution of the Goursat-type problem for the hyperbolic differential equation of the third order with the non-multiple characteristics is obtained in an explicit form.
In the second part, the well-posed Goursat-type problem is considered for a system of the hyperbolic differential equations of the third order. The regular solution of the Goursat-type problem for this system is also obtained in an explicit form.
The theorems for the Hadamard's well-posedness of Goursat-type problem for the hyperbolic differential equation and for a system of the hyperbolic differential equations is formulated as the result of the research.

Keywords: third order hyperbolic equation, non-multiple characteristics, Goursat-type problem, hyperbolic system of third order differential equations, Hadamard correctness.

UDC: 517.956.3

MSC: 74E35, 74K20

Received: December 14, 2018
Revised: February 14, 2019
Accepted: March 4, 2019
First online: March 25, 2019

DOI: 10.14498/vsgtu1666

Bibliographic databases:

• 
• 
• 
• 
• 
•