Semi-Fredholm solvability and asymptotic expansions of singular solutions for Protter problems.

We study four-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of Darboux problems on the plane. It is known that the unique generalized solution may have a strong power-type 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 find asymptotic expansion of the generalized solutions in negative powers of the distance to O. Necessary and sufficient conditions for existence of bounded solutions are derived and additionally some a priori estimates for the singular solutions are given. [ABSTRACT FROM AUTHOR]