Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial Stabilization of Solutions to a Class of Damped Wave
  Equations   We consider a class of wave equations of the type $\partial_{tt} u + Lu +
B\partial_{t} u = 0$, with a self-adjoint operator $L$, and various types of
local damping represented by $B$. By establishing appropriate and raher precise
estimates on the resolvent of an associated operator $A$ on the imaginary axis
of ${{\Bbb C}}$, we prove polynomial decay of the semigroup $\exp(-tA)$
generated by that operator. We point out that the rate of decay depends
strongly on the concentration of eigenvalues and that of the eigenfunctions of
the operator $L$. We give several examples of application of our abstract
result, showing in particular that for a rectangle $\Omega := (0,L_{1})\times
(0,L_{2})$ the decay rate of the energy is different depending on whether the
ratio $L_{1}^2/L_{2}^2$ is rational, or irrational but algebraic.

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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: stat
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex