Exact Behavior of Singularities of Protter’s Problem for the 3-D Wave Equation

For the wave equation we study boundary value problems, which are three-dimensional analogues of Darboux-problems on the plane. It is shown that for n in h there exists a right hand side smooth function from C*(Ω), for which the corresponding unique generalized solution belongs to C*(Ω\O), but it has a strong power-type singularity at the point O. This singularity is isolated at the vertex O of the characteristic cone and does not propagate along the cone. The present article describes the exact behavior of the singular solutions at the point O. It states some exact a priori estimates for the solution.