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Polynomial stability for a system of coupled strings

Rzepnicki, Łukasz; Schnaubelt, Roland


We study the long-time behavior of two vibrating strings which are coupled at a common boundary point by a damper. We show that the classical solutions converge polynomially with a uniform rate, where the decay exponent depends on number theoretic properties of the quotient of the wave speeds of the two springs. The proof is based on a resolvent characterization of polynomial stability due to Borichev–Tomilov and Batty–Duyckaerts.

Volltext §
DOI: 10.5445/IR/1000078186
Veröffentlicht am 21.12.2017
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2017
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000078186
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 20 S.
Serie CRC 1173 ; 2017/35
Schlagwörter polynomial decay, boundary damping, resolvent bound, irrationality measure
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