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On the Asymptotic Behaviour of the Solutions of the Equations of Linear Elastodynamics in Unbounded Domains

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Abstract

We prove, among other things, that if the acoustic tensor satisfies a suitable growth condition at infinity (the hyperbolicity condition) and the total initial energy is summable with a suitable weight, then the solution to the initial boundary value problem of linear elastodynamics in unbounded domains decays at infinity, at every instant, with a rate depending on the weight. Moreover, we show that the hyperbolicity condition is necessary and sufficient for the equipartition in mean of the total energy.

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Authors and Affiliations

  1. Dipartimento di Matematica, Seconda Università degli Studi di Napoli, Via Vivaldi, 43, 81100, Caserta, Italy

    Antonio Russo & Alfonsina Tartaglione

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  1. Antonio Russo
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  2. Alfonsina Tartaglione
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Correspondence to Alfonsina Tartaglione.

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Russo, A., Tartaglione, A. On the Asymptotic Behaviour of the Solutions of the Equations of Linear Elastodynamics in Unbounded Domains. J Elasticity 95, 43–56 (2009). https://doi.org/10.1007/s10659-009-9192-6

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  • DOI: https://doi.org/10.1007/s10659-009-9192-6

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