On Stability of Hyperbolic Thermoelastic Reissner-Mindlin-Timoshenko Plates

Pokojovy, Michael

On Stability of Hyperbolic Thermoelastic Reissner-Mindlin-Timoshenko Plates

Dateien

Pokojovy_253410.pdfGröße: 443.91 KBDownloads: 185

Datum

2013

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Working Paper/Technical Report

Publikationsstatus

Published

Zusammenfassung

In the present article, we consider a thermoelastic plate of Reissner-Mindlin-Timoshenko type with the hyperbolic heat conduction arising from Cattaneo's law. In the absense of any additional mechanical dissipations, the system is often not even strongly stable unless restricted to the rotationally symmetric case, etc. We present a well-posedness result for the linear problem under general mixed boundary conditions for the elastic and thermal parts. For the case of a clamped, thermally isolated plate, we show an exponential energy decay rate under a full damping for all elastic variables. Restricting the problem to the rotationally symmetric case, we further prove that a single frictional damping merely for the bending compoment is sufficient for exponential stability. To this end, we construct a Lyapunov functional incorporating the Bogovskii operator for irrotational vector fields which we discuss in the appendix.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Reissner-Mindlin-Timoshenko plate, hyperbolic thermoelasticity, second sound, exponential stability, rotational symmetry

Zitieren

ISO 690

POKOJOVY, Michael, 2013. On Stability of Hyperbolic Thermoelastic Reissner-Mindlin-Timoshenko Plates

BibTex

@techreport{Pokojovy2013Stabi-25341,
  year={2013},
  series={Konstanzer Schriften in Mathematik},
  title={On Stability of Hyperbolic Thermoelastic Reissner-Mindlin-Timoshenko Plates},
  number={324},
  author={Pokojovy, Michael}
}

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Universitätsbibliographie

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