One dimensional reduction of a renewal equation for a measure-valued function of time describing population dynamics

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Franco , E , Gyllenberg , M & Diekmann , O 2021 , ' One dimensional reduction of a renewal equation for a measure-valued function of time describing population dynamics ' , Acta Applicandae Mathematicae , vol. 175 , no. 1 , 12 . https://doi.org/10.1007/s10440-021-00440-3

Title: One dimensional reduction of a renewal equation for a measure-valued function of time describing population dynamics
Author: Franco, Eugenia; Gyllenberg, Mats; Diekmann, Odo
Other contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2021-10-06
Language: eng
Number of pages: 67
Belongs to series: Acta Applicandae Mathematicae
ISSN: 0167-8019
DOI: https://doi.org/10.1007/s10440-021-00440-3
URI: http://hdl.handle.net/10138/335284
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.
Subject: 111 Mathematics
ASYMPTOTIC-BEHAVIOR
Balanced exponential growth
CELL-GROWTH
Convolution
DISTRIBUTIONS
EXPONENTIAL-GROWTH
FORMULATION
Laplace transform
MODELS
Malthusian parameter
SEMIGROUPS
SIZE DISTRIBUTION
STABILITY
SYSTEM
Volterra integral equations
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