On the stability for linear viscoelastic solids

Giorgi, C.; Lazzari, B.

doi:10.1090/qam/1486541

Authors: C. Giorgi and B. Lazzari
Journal: Quart. Appl. Math. 55 (1997), 659-675
MSC: Primary 73F15; Secondary 45K05, 73H10
DOI: https://doi.org/10.1090/qam/1486541
MathSciNet review: MR1486541
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Abstract: The stability and asymptotic behaviour of solutions to the dynamical initial past-history problem within the theory of linear viscoelasticity is investigated. First, a family of free energies is introduced as a Liapunov functional via the energy method. Then, emphasizing the role of thermodynamic inequalities, the asymptotic stability property is derived by means of some original a priori integral estimates of the solution.

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