Some boundary-value problems for linear multidimensional second-order hyperbolic equations

For the linear hyperbolic equations $$sumlimits_{i,j = 1}^{m + 1} {a_{ij} left( {x,x_{m + 1} } right)u_{x_i x_j } + sumlimits_{i = 1}^{m + 1} {a_i left( {x,x_{m + 1} } right)u_{x_i } + cleft( {x,x_{m + 1} } right)u = 0,x = left( {x_1 ,...,x_m } right)} ,} m geqslant 2,$$ 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.