Exact Asymptotic Expansion of Singular Solutions for the (2+1)-D Protter Problem
Joint Authors
Dechevski, Lubomir
Popov, Todor
Popivanov, Nedyu
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-33, 33 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-06
Country of Publication
Egypt
No. of Pages
33
Main Subjects
Abstract EN
We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in ℝ2.
In contrast to the planar Darboux problem the three-dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of classical solutions.
On the other hand, it is known that for smooth right-hand side functions there is a uniquely determined generalized solution that may have a strong power-type singularity at one boundary point.
This singularity is isolated at the vertex of the characteristic light cone and does not propagate along the cone.
The present paper describes asymptotic expansion of the generalized solutions in negative powers of the distance to this singular point.
We derive necessary and sufficient conditions for existence of solutions with a fixed order of singularity and give a priori estimates for the singular solutions.
American Psychological Association (APA)
Dechevski, Lubomir& Popivanov, Nedyu& Popov, Todor. 2012. Exact Asymptotic Expansion of Singular Solutions for the (2+1)-D Protter Problem. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-33.
https://search.emarefa.net/detail/BIM-459744
Modern Language Association (MLA)
Dechevski, Lubomir…[et al.]. Exact Asymptotic Expansion of Singular Solutions for the (2+1)-D Protter Problem. Abstract and Applied Analysis No. 2012 (2012), pp.1-33.
https://search.emarefa.net/detail/BIM-459744
American Medical Association (AMA)
Dechevski, Lubomir& Popivanov, Nedyu& Popov, Todor. Exact Asymptotic Expansion of Singular Solutions for the (2+1)-D Protter Problem. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-33.
https://search.emarefa.net/detail/BIM-459744
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-459744