Geodesic
The Goursat-type problem for a hyperbolic equation and~system of third order hyperbolic equations
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 1, pp. 186-194

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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, hyperbolic system of third order differential equations, Hadamard correctness.
Mots-clés : Goursat-type problem 
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     title = {The {Goursat-type} problem for a hyperbolic equation and~system of third order hyperbolic equations},
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A. A. Andreev; J. O. Yakovleva. The Goursat-type problem for a hyperbolic equation and~system of third order hyperbolic equations. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 1, pp. 186-194. http://geodesic.mathdoc.fr/item/VSGTU_2019_23_1_a9/