Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Asymptotic behaviour in linear viscoelasticity

Author: Jaime E. Muñoz Rivera
Journal: Quart. Appl. Math. 52 (1994), 628-648
MSC: Primary 73F15; Secondary 35B40, 35Q72, 45K05
DOI: https://doi.org/10.1090/qam/1306041
MathSciNet review: MR1306041
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Abstract: We study the asymptotic behaviour of the solution of the viscoelastic equation, and we prove for a bounded domain that the energy associated to this system approaches zero exponentially as time goes to infinity. Moreover, for the whole space $ {\mathbb{R}^n}$ we will prove that the displacement vector field can be decomposed into two parts, solenoidal and irrotational, whose corresponding energies decay to zero uniformly as time goes to infinity with rates that depend on the regularity of the initial data.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/1306041
Article copyright: © Copyright 1994 American Mathematical Society