### 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 language | English |
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Pages (from-to) | 215-228 |

Number of pages | 14 |

Journal | Note di Matematica |

Volume | 27 |

Issue number | 2 |

Publication status | Published - Dec 1 2007 |

### Keywords

- Laplace transform
- Linear viscoelasticity
- Renewal equation
- Resolvent

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'On exact rates of growth and decay of solutions of a linear Volterra equation in linear viscoelasticity'. Together they form a unique fingerprint.

## Cite this

Reynolds, D. W., Appleby, J. A. D., & Gyori, I. (2007). On exact rates of growth and decay of solutions of a linear Volterra equation in linear viscoelasticity.

*Note di Matematica*,*27*(2), 215-228.