On exact rates of decay of solutions of linear systems of Volterra equations with delay

John A D Appleby, I. Győri, David W. Reynolds

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

This paper considers the resolvent of a finite-dimensional linear convolution Volterra integral equation. The main results give conditions which ensure that the exact rate of decay of the resolvent can be determined using a positive weight function related to the kernel. The decay rates can be exponential or subexponential. Many other related results on exact rates of exponential and subexponential decay of solutions of Volterra integro-differential equations are given. We also present an application to a linear compartmental system with discrete and continuous lags.

Original languageEnglish
Pages (from-to)56-77
Number of pages22
JournalJournal of Mathematical Analysis and Applications
Volume320
Issue number1
DOIs
Publication statusPublished - Aug 1 2006

Fingerprint

Decay of Solutions
Volterra Equation
Integrodifferential equations
Resolvent
Convolution
Integral equations
Linear systems
Linear Systems
Volterra Integro-differential Equations
Volterra Integral Equations
Decay Rate
Weight Function
Decay
kernel

Keywords

  • Asymptotic behaviour
  • Characteristic equations
  • Subexponential distributions
  • Subexponential functions
  • Volterra integral equations
  • Volterra integro-differential equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

On exact rates of decay of solutions of linear systems of Volterra equations with delay. / Appleby, John A D; Győri, I.; Reynolds, David W.

In: Journal of Mathematical Analysis and Applications, Vol. 320, No. 1, 01.08.2006, p. 56-77.

Research output: Contribution to journalArticle

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