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Stability and exponential stability in linear viscoelasticity

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Abstract

In this survey paper, we discuss the decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation

$${\partial_{tt}}u(t) - \Delta u(t) + {\int_0^\infty} \mu(s) \Delta u(t - s) {\rm{d}}s = 0$$

describing the dynamics of linearly viscoelastic bodies.

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Authors and Affiliations

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

    Vittorino Pata

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  1. Vittorino Pata
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Correspondence to Vittorino Pata.

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Dedicated to the memory of Professor Giovanni Prouse

Work partially supported by the Italian PRIN Research Project 2006 Problemi a frontiera libera, transizioni di fase e modelli di isteresi.

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Pata, V. Stability and exponential stability in linear viscoelasticity. Milan J. Math. 77, 333–360 (2009). https://doi.org/10.1007/s00032-009-0098-3

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  • DOI: https://doi.org/10.1007/s00032-009-0098-3

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