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2014 Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem
Nedyu Popivanov, Todor Popov, Allen Tesdall
Abstr. Appl. Anal. 2014(SI62): 1-19 (2014). DOI: 10.1155/2014/260287

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.

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Nedyu Popivanov. Todor Popov. Allen Tesdall. "Semi-Fredholm Solvability in the Framework of Singular Solutions for the (3+1)-D Protter-Morawetz Problem." Abstr. Appl. Anal. 2014 (SI62) 1 - 19, 2014. https://doi.org/10.1155/2014/260287

Information

Published: 2014
First available in Project Euclid: 27 February 2015

zbMATH: 07022029
MathSciNet: MR3272190
Digital Object Identifier: 10.1155/2014/260287

Rights: Copyright © 2014 Hindawi

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Vol.2014 • No. SI62 • 2014
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