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Can the Average Temperature Stabilize a System of Thermoelastic Plates?

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Abstract

We consider a system of thermoelastic plates with the same conductivity. The coupling in each plate component involves the average temperature of all the plates in the system. We show that if the coefficients of flexural rigidity are pairwise distinct, then the system underlying semigroup is exponentially stable. This is done first for the Fourier model, and then for the Maxwell–Cattaneo model. In particular, for the Maxwell–Cattaneo model, exponential stability is established when the rotational inertia is accounted for, while only polynomial stability is established otherwise. We use a combination of the multiplier techniques and the frequency domain method to prove all results.

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Acknowledgements

The author would like to take this opportunity to express his thanks to Professor Enrique Zuazua for his constant friendship and support, since they first met more than two decades ago.

The author is also indebted to the anonymous referees whose thoughtful feedback has been very helpful in the final presentation of this work.

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  1. Department of Mathematics and Statistics, Florida International University, Modesto Maidique Campus, Miami, FL, 33199, USA

    Louis Tebou

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  1. Louis Tebou
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Correspondence to Louis Tebou.

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This work is a tribute to Professor Enrique Zuazua on the occasion of his sixtieth birthday.

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Tebou, L. Can the Average Temperature Stabilize a System of Thermoelastic Plates?. Vietnam J. Math. 49, 787–814 (2021). https://doi.org/10.1007/s10013-021-00494-8

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