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Transmission problems in (thermo-)viscoelasticity with Kelvin-Voigt damping : non-exponential, strong and polynomial stability

Transmission problems in (thermo-)viscoelasticity with Kelvin-Voigt damping : non-exponential, strong and polynomial stability

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MUNOZ RIVERA, Jaime E., Reinhard RACKE, 2015. Transmission problems in (thermo-)viscoelasticity with Kelvin-Voigt damping : non-exponential, strong and polynomial stability

@techreport{Munoz Rivera2015Trans-30731, series={Konstanzer Schriften in Mathematik}, title={Transmission problems in (thermo-)viscoelasticity with Kelvin-Voigt damping : non-exponential, strong and polynomial stability}, year={2015}, number={336}, author={Munoz Rivera, Jaime E. and Racke, Reinhard} }

Racke, Reinhard Racke, Reinhard We investigate transmission problems between a (thermo-)viscoelastic system with Kelvin-Voigt damping, and a purely elastic system. It is shown that neither the elastic damping by Kelvin-Voigt mechanisms nor the dissipative effect of the temperature in one material can assure the exponential stability of the total system when it is coupled through transmission to a purely elastic system. The approach shows the lack of exponential stability using Weyl's theorem on perturbations of the essential spectrum. Instead, strong stability can be shown using the principle of unique continuation. To prove polynomial stability we provide an extended version of the characterizations by Borichev and Tomilov. Observations on the lack of compacity of the inverse of the arising semigroup generators are included too. The results apply to thermo-viscoelastic systems, to< purely elastic systems as well as to the scalar case consisting of wave equations. Munoz Rivera, Jaime E. 2015-04-14T09:09:04Z Munoz Rivera, Jaime E. eng 2015-04-14T09:09:04Z Transmission problems in (thermo-)viscoelasticity with Kelvin-Voigt damping : non-exponential, strong and polynomial stability 2015

Dateiabrufe seit 14.04.2015 (Informationen über die Zugriffsstatistik)

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