Well-posedness of many-dimensional Darboux problems for degenerating hyperbolic equations - Aldashev, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
Forthe equation ^m_i=tt^k_iU_x_i,x_i - U_n + ^m_i=t a_i(x,t)U_x_i + b(x, t)u_t + c(x,t)u = 0, k_i = 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_i(x,t) = O(1)t^α, i = 1,..., m, α >k_12 - 2. We prove that if this condition is satisfied, then the Darboux problems are uniquely solvable.