## Abstract and Applied Analysis

### Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem

#### Abstract

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 $O$ 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 $O$. Some necessary and sufficient conditions for existence of bounded solutions are proven and additionally a priori estimates for the singular solutions are obtained.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 260287, 19 pages.

Dates
First available in Project Euclid: 27 February 2015

https://projecteuclid.org/euclid.aaa/1425047824

Digital Object Identifier
doi:10.1155/2014/260287

Mathematical Reviews number (MathSciNet)
MR3272190

Zentralblatt MATH identifier
07022029

#### Citation

Popivanov, Nedyu; Popov, Todor; Tesdall, Allen. Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 260287, 19 pages. doi:10.1155/2014/260287. https://projecteuclid.org/euclid.aaa/1425047824

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