Correctness of multi-dimensional Darboux problems for the wave equation

• Date: 1993
• Main Authors: Aldashev, S. A., Алдашев, С. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5933
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.