The Dirichlet Problem for the Semilinear Vibrating String Equation in a Class of Domains with Corner Points

This paper deals with existence, uniqueness, and regularity of solutions of the Dirichlet problem for the semilinear vibrating string equation in a class of bounded domains with corner points, Under some symmetry conditions on the boundary we reduce our problem to the corresponding problem in a rect...

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Veröffentlicht in:	Journal of mathematical analysis and applications 1995-02, Vol.189 (3), p.872-896
Hauptverfasser:	Lyashenko, A.A., Smiley, M.W.
Format:	Artikel
Sprache:	eng
Schlagworte:	Classical and quantum physics: mechanics and fields Classical mechanics of continuous media: general mathematical aspects Exact sciences and technology Function theory, analysis Mathematical analysis Mathematical methods in physics Mathematics Partial differential equations Physics Sciences and techniques of general use Vibrations and mechanical waves Waves and wave propagation: general mathematical aspects
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Beschreibung
Zusammenfassung:	This paper deals with existence, uniqueness, and regularity of solutions of the Dirichlet problem for the semilinear vibrating string equation in a class of bounded domains with corner points, Under some symmetry conditions on the boundary we reduce our problem to the corresponding problem in a rectangle. Using known results for rectangular domains, existence, uniqueness, and regularity of solutions are obtained.
ISSN:	0022-247X 1096-0813
DOI:	10.1006/jmaa.1995.1055