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Asymptotic behaviour of a semilinear viscoelastic beam model

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Abstract.

The asymptotic behaviour of a model for a viscoelastic beam with nonlinear load is studied. Under the assumptions that the energy is coercive and the solution set of the stationary problem is discrete, the convergence of the solutions of the dynamical problem to a steady state are shown. To prove this statement, a method known for problems in finite dimensions is combined with results about the corresponding linear problem, energy estimates for the nonlinear problem, and harmonic analysis of vector-valued functions.

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Authors and Affiliations

  1. Department of Mathematical Analysis, Charles University, Sokolovská 83, Cz-18600 Praha 8,¶ Czech Republic, , , , , , CZ

    E. Fašangová

  2. Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg,¶ Theodor-Lieser Str. 5, D-60120 Halle, Germany, , , , , , DE

    J. Prüss

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  1. E. Fašangová
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  2. J. Prüss
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Eingegangen am 1. 4. 1998

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Fašangová, E., Prüss, J. Asymptotic behaviour of a semilinear viscoelastic beam model. Arch. Math. 77, 488–497 (2001). https://doi.org/10.1007/PL00000522

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  • DOI: https://doi.org/10.1007/PL00000522

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