The Goursat problem for second-order hyperbolic systems with nonsplitting leading parts (Q1874854)

The well posedness of the Goursat problem for a second-order linear hyperbolic homogeneous system of differential equations with constant coefficients in a domain bounded by segments of the characteristics of the system is investigated. For sufficiently smooth boundary vector functions and under the assumption that coefficients satisfy some additional conditions, the Goursat problem is well posed. Two such results -- necessary and sufficient conditions -- are proved. The author refers to the results and proofs of \textit{M. Kh. Shkhanukov} [Differ. Uravn. 21, 169-172 (1985; Zbl 0583.35072)].