Well-posedness of many-dimensional Darboux problems for degenerating hyperbolic equations

• Date: 1994
• Main Authors: Aldashev, S. A., Алдашев, С. А.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1994
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5607
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Forthe equation $$\sum^{m}_{i=t}t^{k_i}U_{x_i,x_i} - U_n + \sum^{m}_{i=t} a_i(x,t)U_{x_i} + b(x, t)u_t + c(x,t)u = 0,$$ $$k_i = \text{const} ≥ 0,\; i = l ..... m, x = (x_1,..., x_m),\; m_>2,$$ we find a many-dimensional analog of the well-known "Gellerstedt condition" $$ a_...