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We study four-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of Darboux problems on the plane. They were formulated by M.H.Protter in connection with BVPs for mixed type equations that model transonic flow phenomena. It is known that the unique generalized solution of Protter's problem may have singularity at only one point. This singularity is isolated at the vertex O of the boundary light characteristic cone and does not propagate along the cone. We present some conditions on the smooth right-hand side functions that are sufficient for existence of generalized solutions and give some a priori estimates for its singularity at O. [ABSTRACT FROM AUTHOR]