On exact rates of growth and decay of solutions of a linear Volterra equation in linear viscoelasticity

David W. Reynolds, John A.D. Appleby, István Gyori

Research output: Contribution to journalArticle

Abstract

The asymptotic behaviour of a scalar linear nonconvolution Volterra equation is investigated; the equation is that satisfied by the modes of a viscoelastic rod bending quasistatically. A sufficient condition for the trivial solution to be asymptotic stable is given, as well as results on describing the exact rate of decay: in the case that the trivial solution is unstable, the exact rate of growth of solutions is specified.

Original languageEnglish
Pages (from-to)215-228
Number of pages14
JournalNote di Matematica
Volume27
Issue number2
Publication statusPublished - Dec 1 2007

Keywords

  • Laplace transform
  • Linear viscoelasticity
  • Renewal equation
  • Resolvent

ASJC Scopus subject areas

  • Mathematics(all)

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