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We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems inℝ2. In contrast to the planar Darboux problem the three-dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of classical solutions. On the other hand, it is known that for smooth right-hand side functions there is a uniquely determined generalized solution that may have a strong power-type singularity at onedoi:10.1155/2012/278542 fatcat:teon75a6cnagdiwskq65nosojm