On the solvability of the Goursat problem for one class of loaded second-order hyperbolic equations

Abstract

In this paper the solvability of the Goursat problems for two locally loaded second-order hyperbolic equations with a wave operator in the main part was explored. The loaded terms for both equations have the same trace, namely a part of one of the characteristics for the given hyperbolic operator, but the traceforming maps are different. Moreover, in the first case, any point of the domain under consideration and the corresponding point of the load trace always lie on a straight line, which is a characteristic. In the second case, this does not work. It turns out that in the first case the Goursat problem is Voltairean, and in the second case it is Fredholmian.