Correctness of multi-dimensional Darboux problems for the wave equation

Abstract

It is proved that multi-dimensional Darboux problems for the wave equation are correct in the domain $D_3 \subset E_{m + 1}$ bounded by the surfaces ¦x ¦=t + ɛ and ¦x ¦=1- t and the plane t = 0, 0 ≤ ɛ < 1. The behavior of the solutions as ɛ → 0 is studied.