The Goursat-type problem for a hyperbolic equation and system of third order hyperbolic equations
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 ord...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Samara State Technical University
2019-12-01
|
| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/34686/23035 |
| Summary: | 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. |
|---|---|
| ISSN: | 1991-8615 2310-7081 |