One multidimensional version of the Darboux first problem for one class of semilinear second order hyperbolic systems

Abstract

Abstract.One multidimensional version of the Darboux first problem for one class of semilinear second order hyperbolic systems is investigated. The questions on local and global solvability and nonexistence of a global solution of this problem are considered. Mathematics Subject Classification. 35L51, 35L71.Keywords. Multidimensional version of the Darboux first problem, Semilinear second order hyperbolic systems, Local and global solvability, Nonexistence of a global solution.