Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth attractors of finite dimension for von Karman evolutions with
  nonlinear frictional damping localized in a boundary layer   In this paper dynamic von Karman equations with localized interior damping
supported in a boundary collar are considered. Hadamard well-posedness for von
Karman plates with various types of nonlinear damping are well-known, and the
long-time behavior of nonlinear plates has been a topic of recent interest.
Since the von Karman plate system is of "hyperbolic type" with critical
nonlinearity (noncompact with respect to the phase space), this latter topic is
particularly challenging in the case of geometrically constrained and nonlinear
damping. In this paper we first show the existence of a compact global
attractor for finite-energy solutions, and we then prove that the attractor is
both smooth and finite dimensional. Thus, the hyperbolic-like flow is
stabilized asymptotically to a smooth and finite dimensional set.
  Key terms: dynamical systems, long-time behavior, global attractors,
nonlinear plates, nonlinear damping, localized damping

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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc