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Singular Solutions to a (3 + 1)-D Protter-Morawetz Problem for Keldysh-Type Equations

Popivanov, Nedyu; Hristov, Tsvetan; Nikolov, Aleksey; Schneider, Manfred

Abstract:
We study a boundary value problem for (3 + 1)-D weakly hyperbolic equations of Keldysh type (problem PK). The Keldysh-type equations are known in some specific applications in plasma physics, optics, and analysis on projective spaces. Problem PK is not well-posed since it has infinite-dimensional cokernel. Actually, this problem is analogous to a similar one proposed by M. Protter in 1952, but for Tricomi-type equations which, in part, are closely connected with transonic fluid dynamics.We consider a properly defined, in a special function space, generalized solution to problem PK for which existence and uniqueness theorems hold. It is known that it may have a strong power-type singularity at one boundary point even for very smooth right-hand sides of the equation. In the present paper we study the asymptotic behavior of the generalized solutions of problem PK at the singular point. There are given orthogonality conditions on the right-hand side of the equation, which are necessary and sufficient for the existence of a generalized solution with fixed order of singularity.

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Verlagsausgabe §
DOI: 10.5445/IR/1000079782
Veröffentlicht am 16.11.2018
Originalveröffentlichung
DOI: 10.1155/2017/1571959
Scopus
Zitationen: 8
Web of Science
Zitationen: 8
Zugehörige Institution(en) am KIT Fakultät für Mathematik (MATH)
Publikationstyp Zeitschriftenaufsatz
Jahr 2017
Sprache Englisch
Identifikator ISSN: 1687-9120, 1687-9139
urn:nbn:de:swb:90-797825
KITopen-ID: 1000079782
Erschienen in Advances in mathematical physics
Band 2017
Seiten Art.Nr.: 1571959
Nachgewiesen in Web of Science
Scopus
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