KOPS - The Institutional Repository of the University of Konstanz

On Exponential Stability for Thermoelastic Plates : Comparison and Singular Limits

On Exponential Stability for Thermoelastic Plates : Comparison and Singular Limits

Cite This

Files in this item

Files Size Format View

There are no files associated with this item.

MUNOZ RIVERA, Jaime E., Reinhard RACKE, Mauricio SEPULVEDA, Octavio VERA VILLAGRAN, 2020. On Exponential Stability for Thermoelastic Plates : Comparison and Singular Limits. In: Applied Mathematics & Optimization. Springer. ISSN 0095-4616. eISSN 1432-0606. Available under: doi: 10.1007/s00245-020-09670-7

@article{MunozRivera2020Expon-41867.2, title={On Exponential Stability for Thermoelastic Plates : Comparison and Singular Limits}, year={2020}, doi={10.1007/s00245-020-09670-7}, issn={0095-4616}, journal={Applied Mathematics & Optimization}, author={Munoz Rivera, Jaime E. and Racke, Reinhard and Sepulveda, Mauricio and Vera Villagran, Octavio} }

Sepulveda, Mauricio eng terms-of-use 2020 Munoz Rivera, Jaime E. 2020-04-23T08:16:21Z On Exponential Stability for Thermoelastic Plates : Comparison and Singular Limits We consider different models of thermoelastic plates in a bounded reference configuration: with Fourier heat conduction or with the Cattaneo model, and with or without inertial term. Some models exhibit exponential stability, others are not exponential stable. In the cases of exponential stability, we give an explicit estimate for the rate of decay in terms of the essential parameters appearing (delay τ≥0 τ≥0 , inertial constant μ≥0 μ≥0 ). This is first done using multiplier methods directly in L<sup>2</sup> -spaces, then, second, with eigenfunction expansions imitating Fourier transform techniques used for related Cauchy problems; also here essentially energy estimates are used, a spectral analysis is avoided. The explicit estimates allow for a comparison. The singular limits τ→0 τ→0 , and μ→0 μ→0 are also investigated in order to understand the mutual relevance for the (non-) exponential stability of the models. Numerical simulations underline the results obtained analytically, and exhibit interesting coincidences of analytical and numerical estimates, respectively. Munoz Rivera, Jaime E. Vera Villagran, Octavio Racke, Reinhard Sepulveda, Mauricio 2020-04-23T08:16:21Z Vera Villagran, Octavio Racke, Reinhard

This item appears in the following Collection(s)

Version History

Version Item Date Summary Publication Version

*Selected version

Search KOPS


Browse

My Account