On some boundary value problems for linear multidimensional hyperbolic equations of the second order - Aldashev , S. A. (Ukrains’kyi Matematychnyi Zhurnal, 1991)
For the linear hyperbolic equations\[\sum_{i,j=1}^{m+1} a_{ij}(x,x_{m+1})u_{x_ix_j}+\sum_{i=1}^{m+1} a_i(x,x_{m+1})u_{x_i}+c(x,x_{m+1})u=0, \]\[x=(x_1,\dots,x_m), \, m\geq2\]the correctness of multidimensional analogues of the problems of Darboux and Goursat is established and a theorem on the uniqueness of a solution of the Cauchy characteristic problem is proved.