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Heat–Viscoelastic Plate Interaction via Bending Moment and Shear Forces Operators: Analyticity, Spectral Analysis, Exponential Decay

  • Roberto TriggianiEmail author
Article

Abstract

We consider a heat–plate interaction model where the 2-dimensional plate is subject to viscoelastic (strong) damping. Coupling occurs at the interface between the two media, where each component evolves through differential operators. In this paper, we apply “high” boundary interface conditions, which involve the two classical boundary operators of a physical plate: the bending moment operator \(B_1\) and the shear forces operator \(B_2\). We prove three main results: analyticity of the corresponding contraction semigroup on the natural energy space; sharp location of the spectrum of its generator, which does not have compact resolvent, and has the point \(\lambda =-\,1\) in its continuous spectrum; exponential decay of the semigroup with sharp decay rate. Here analyticity cannot follow by perturbation.

Keywords

Heat–viscoelastic interaction Analyticity Exponential decay 

Notes

Acknowledgements

Research partially supported by the National Science Foundation under Grant DMS-1713506. The author wishes to thank two referees for their comments.

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Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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