On the singularities of 3-D Protter's problem for the wave equation

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dc.contributor.authorGrammatikopoulos, Myron K.
dc.contributor.authorHristov, Tzvetan D.
dc.contributor.authorPopivanov, Nedyu I.
dc.date.accessioned2021-05-17T19:11:38Z
dc.date.available2021-05-17T19:11:38Z
dc.date.issued2001-01-01
dc.description.abstractIn this paper we study boundary-value problems for the wave equation, which are three-dimensional analogue of Darboux-problems (or of Cauchy-Goursat problems) on the plane. It is shown that for n in ℕ there exists a right hand side smooth function from Cn(Ω̅0), for which the corresponding unique generalized solution belongs to Cn(Ω̅0)O), and 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. In this paper we investigate the behavior of the singular solutions at the point O. Also, we study more general boundary-value problems and find that there exist an infinite number of smooth right-hand side functions for which the corresponding unique generalized solutions are singular. Some a priori estimates are also stated.
dc.description.departmentMathematics
dc.formatText
dc.format.extent26 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationGrammatikopoulos, M. K., Hristov, T. D., & Popivanov, N. I. (2001). On the singularities of 3-D Protter's problem for the wave equation. <i>Electronic Journal of Differential Equations, 2001</i>(01), pp. 1-26.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/13569
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2001, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectWave equation
dc.subjectBoundary-value problems
dc.subjectGeneralized solution
dc.subjectSingular solutions
dc.subjectPropagation of singularities
dc.titleOn the singularities of 3-D Protter's problem for the wave equation
dc.typeArticle

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