| Abstract: |
| We consider a fluid-plate interaction model where the two dimensional plate is subject to viscoelastic (strong) damping. We prove four main results: $(i)$ analyticity, on the natural energy space, of the corresponding contraction semigroup (and of its adjoint); $(ii)$ sharp location of the spectrum of its generator (and similarly of the adjoint generator), neither of which has compact resolvent, and in fact both of which have the point $ \\lambda = -\\frac{1}{\\rho}$ in their respective continuous spectrum; $(iii)$ both original generator and its adjoint have the origin $\\lambda =0 $ as a common eigenvalue with a common, explicit, 1-dimensional eigenspace; $(iv)$ The subspace of codimension 1 obtained by the original energy space by factoring out the common 1-dimensional eigenspace is invariant under the action of the (here restricted) semigroup (or of its adjoint), and on such subspace both original and adjoint semigroups are uniformly stable. |
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