On spatial behavior in linear viscoelasticity

Galeş, Cătălin; Chiriţă, Stan

doi:10.1090/S0033-569X-09-01149-0

Authors: Cătălin Galeş and Stan Chiriţă
Journal: Quart. Appl. Math. 67 (2009), 707-723
MSC (2000): Primary 74D05, 74G50; Secondary 74H45, 74E10
DOI: https://doi.org/10.1090/S0033-569X-09-01149-0
Published electronically: May 12, 2009
MathSciNet review: 2588231
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Abstract: Within the framework of linear viscoelasticity this paper deals with the study of spatial behavior of solutions describing harmonic vibrations in a right cylinder of finite extent. Some exponential decay estimates of Saint–Venant type, in terms of the distance from the excited end of the cylinder are obtained from a first-order differential inequality concerning an appropriate measure associated with the amplitude of the steady-state vibration. The dissipative mechanism guarantees the validity of the result for every value of the frequency of vibration and for the class of viscoelastic materials compatible with thermodynamics whose relaxation tensor is supposed to be symmetric and sufficiently regular. The case of a semi-infinite cylinder is also studied, and some alternatives of Phragmén–Lindelöf type are established.

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