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For the four-dimensional nonhomogeneous wave equation boundary value problems that are multidimensional analogues of Darboux problems in the plane are studied. It is known that for smooth right-hand side functions the unique generalized solution may have a strong power-type singularity at only one point. This singularity is isolated at the vertex �� of the boundary light characteristic cone and does not propagate along the bicharacteristics.The present paper describes asymptotic expansions of the generalized solutions in negative powers of the distance to ��. Some necessary and sufficient conditions for existence of bounded solutions are proven and additionally a priori estimates for the singular solutions are obtained.


This work was originally published in Abstract and Applied Analysis, available at DOI: 10.1155/2014/260287.

This is an open access article distributed under the Creative Commons Attribution License 3.0 (CC BY 3.0).

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