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

• Main Authors: Aleksandr A. Andreev, Juliya O. Yakovleva
• Format: Article
• Language: English
• Published: Samara State Technical University 2019-03-01
• Series: Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
• Subjects: third order hyperbolic equation; non-multiple characteristics; goursat-type problem; hyperbolic system of third order differential equations; hadamard correctness
• Online Access: http://mi.mathnet.ru/eng/vsgtu1666

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.