OS Partielle Differentialgleichungen: Exponential stability for thermoelastic plates: comparison and singular limits
Wann
Donnerstag, 24. Mai 2018
15:15 bis 16:45 Uhr
Wo
F 426
Veranstaltet von
Vortragende Person/Vortragende Personen:
Prof. Dr. Reinhard Racke (Universität Konstanz)
Diese Veranstaltung ist Teil der Veranstaltungsreihe „Oberseminar Partielle Differentialgleichungen“.
Abstract: We consider di fferent models of thermoelastic plates in a bounded reference con figuration: 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, inertial constant μ≥0). This is rst done using multiplier methods directly in L2-spaces, then, second, with eigenfunction expansions imitating Fourier transform techniques used for related Cauchy problems. The explicit estimates allow for a comparison. The singular limits τ→0, and 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.