One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics

Eugenia Franco*, Mats Gyllenberg, Odo Diekmann

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Despite their relevance in mathematical biology, there are, as yet, few general results about the asymptotic behaviour of measure valued solutions of renewal equations on the basis of assumptions concerning the kernel. We characterise, via their kernels, a class of renewal equations whose measure-valued solution can be expressed in terms of the solution of a scalar renewal equation. The asymptotic behaviour of the solution of the scalar renewal equation, is studied via Feller’s classical renewal theorem and, from it, the large time behaviour of the solution of the original renewal equation is derived.

Original languageEnglish
Article number12
Pages (from-to)1-67
Number of pages67
JournalActa Applicandae Mathematicae
Volume175
Issue number1
DOIs
Publication statusPublished - Oct 2021

Keywords

  • Balanced exponential growth
  • Convolution
  • Laplace transform
  • Malthusian parameter
  • Volterra integral equations

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