TY - JOUR

T1 - One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics

AU - Franco, Eugenia

AU - Gyllenberg, Mats

AU - Diekmann, Odo

N1 - Funding Information:
Open access funding provided by University of Helsinki including Helsinki University Central Hospital. The research was supported by the Atmospheric Mathematics (AtMath) collaboration of the Faculty of Science of the University of Helsinki, the Horizon 2020 ERC project as well as the Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research (project No. 307333)
Publisher Copyright:
© 2021, The Author(s).

PY - 2021/10

Y1 - 2021/10

N2 - 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.

AB - 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.

KW - Balanced exponential growth

KW - Convolution

KW - Laplace transform

KW - Malthusian parameter

KW - Volterra integral equations

U2 - 10.1007/s10440-021-00440-3

DO - 10.1007/s10440-021-00440-3

M3 - Article

AN - SCOPUS:85116426839

SN - 0167-8019

VL - 175

SP - 1

EP - 67

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

IS - 1

M1 - 12

ER -