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Asymptotic behavior of coupled linear systems modeling suspension bridges

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Abstract

We consider the coupled linear system

$$\left\{\begin{array}{ll} \partial_{tt} u + \partial_{xxxx}u + \gamma \partial_t u + k(u - v) + h\partial_{t} (u-v) = 0\\\epsilon \partial_{tt} v - \partial_{xx}v - k(u - v) - h\partial_{t} (u - v) = 0\end{array}\right.$$

describing the vibrations of a string-beam system related to the well-known Lazer–McKenna suspension bridge model. For ε > 0 and k > 0, the decay properties of the solution semigroup are discussed in dependence of the nonnegative parameters γ and h, which are responsible for the damping effects.

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Authors and Affiliations

  1. DICATAM, Università di Brescia, Via Valotti 9, 25133, Brescia, Italy

    Filippo Dell’Oro & Claudio Giorgi

  2. Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Via Bonardi 9, 20133, Milan, Italy

    Vittorino Pata

Authors
  1. Filippo Dell’Oro
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  2. Claudio Giorgi
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  3. Vittorino Pata
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Correspondence to Claudio Giorgi.

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Dell’Oro, F., Giorgi, C. & Pata, V. Asymptotic behavior of coupled linear systems modeling suspension bridges. Z. Angew. Math. Phys. 66, 1095–1108 (2015). https://doi.org/10.1007/s00033-014-0414-9

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  • DOI: https://doi.org/10.1007/s00033-014-0414-9

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