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On a Kelvin-Voigt viscoelasticwave equation with strong delay

Anikushyn, Andrii; Demchenko, Anna; Pokojovy, Michael


An initial-boundary value problem for a viscoelastic wave equation subject to a strong timelocalized
delay in a Kelvin & Voigt-type material law is considered. Transforming the equation
to an abstract Cauchy problem on the extended phase space, a global well-posedness theory
is established using the operator semigroup theory both in Sobolev-valued C0- and BV-spaces.
Under appropriate assumptions on the coefficients, a global exponential decay rate is obtained
and the stability region in the parameter space is further explored using the Lyapunov’s indirect
method. The singular limit τ -> 0 is further studied with the aid of the energy method. Finally,
a numerical example from a real-world application in biomechanics is presented.

Volltext §
DOI: 10.5445/IR/1000086920
Veröffentlicht am 24.10.2018
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000086920
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 34 S.
Serie CRC 1173 ; 2018/27
Schlagwörter wave equation, Kelvin-Voigt damping, time-localized delay, well-posedness, exponential stability, singular limit
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