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用于描述种群动态的时间测度值函数的更新方程的一维约简

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

作者信息

Franco Eugenia, Gyllenberg Mats, Diekmann Odo

机构信息

Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland.

Mathematical Institute, Utrecht University, Utrecht, Netherlands.

出版信息

Acta Appl Math. 2021;175(1):12. doi: 10.1007/s10440-021-00440-3. Epub 2021 Oct 6.

DOI:10.1007/s10440-021-00440-3
PMID:34720280
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8547227/
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.

摘要

尽管它们在数学生物学中具有相关性，但基于关于核的假设，关于更新方程的测度值解的渐近行为，目前还几乎没有一般性的结果。我们通过其核来刻画一类更新方程，这类更新方程的测度值解可以用一个标量更新方程的解来表示。通过费勒的经典更新定理研究标量更新方程解的渐近行为，并由此推导出原更新方程解的长时间行为。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f66a/8547227/6411b74e451a/10440_2021_440_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f66a/8547227/ce111130cd67/10440_2021_440_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f66a/8547227/d401af214202/10440_2021_440_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f66a/8547227/66a3b2461b4c/10440_2021_440_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f66a/8547227/a4b8b2596231/10440_2021_440_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f66a/8547227/6411b74e451a/10440_2021_440_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f66a/8547227/ce111130cd67/10440_2021_440_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f66a/8547227/d401af214202/10440_2021_440_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f66a/8547227/66a3b2461b4c/10440_2021_440_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f66a/8547227/a4b8b2596231/10440_2021_440_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/f66a/8547227/6411b74e451a/10440_2021_440_Fig5_HTML.jpg

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