2018
DOI: 10.3934/eect.2018008
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Heat-viscoelastic plate interaction: Analyticity, spectral analysis, exponential decay

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 components evolves. In this paper, we apply "low", physically hinged boundary interface conditions, which involve the bending moment operator for the plate. 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 … Show more

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Cited by 13 publications
(4 citation statements)
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“…Several examples of this kind can be found in the literature. For instance, we address the reader to the works [1,3,4,5,6,11,12,16,18,20,22,27,28,29,30,31,32,33,37,40], just to name a few. In some of these contributions, the dissipation is not mechanical, but only thermal through a heat equation of Fourier type.…”
Section: A General Discussionmentioning
confidence: 99%
“…Several examples of this kind can be found in the literature. For instance, we address the reader to the works [1,3,4,5,6,11,12,16,18,20,22,27,28,29,30,31,32,33,37,40], just to name a few. In some of these contributions, the dissipation is not mechanical, but only thermal through a heat equation of Fourier type.…”
Section: A General Discussionmentioning
confidence: 99%
“…Earlier results. Although there is a vast literature concerning systems of coupled conservative-dissipative equations (e.g., [1,2,4,6,7,11,12,19,30], just to name a few), the behavior of systems like (2.1) remains largely unexplored. One paper in that direction is [9], dealing with the ODE model…”
Section: Introductionmentioning
confidence: 99%
“…The coupling allows the transfer of dissipation, so that the system becomes globally stable as time tends to infinity. Just to quote some results in this direction, we mention the papers [1,2,3,4,5,6,7,8,9,11,13,15,18,19] and the book [14], but the list is far from being exhaustive. Perhaps, the simplest example is given by an ideal oscillator without damping, coupled by velocities with a physical oscillator subject to dynamical friction, with initial conditions assigned at time t = 0.…”
mentioning
confidence: 99%