A regularization scheme for an inverse problem in age-structured populations
type: Item
instance of: scholarly article
title: A regularization scheme for an inverse problem in age-structured populations
zbMATH Open document ID: 0841.92021
author: Heinz W. Engl
author: William Rundell
author: Otmar Scherzer
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-07-16T00:00:00Z
review text: In many models describing the evolution of species it is necessary to allow the birth and death processes to depend on the age of the individual. We then have an age-structured population where \(\rho (a,t)\) denotes the number of individuals of age \(a\) at a particular time \(t\). We denote by \(\beta = \beta (a)\) and \(\lambda = \lambda (a)\) the birth and death functions of the species -- the quantities \(\lambda (a) da\) and \(\beta (a) da\) correspond to the probabilities of an individual of age \(a\) dying or giving birth on the interval \([a,a + da]\), respectively. The usual direct problem for age-structured populations is to be given the ``birth'' and ``death'' functions \(\beta (\cdot)\) and \(\lambda (\cdot)\), as well as the initial value \(\varphi (a)\), and use these to recover \(\rho (a,t)\) for \(t > 0\). We let \(L\) denote the maximum life span of the species, that is, \(\rho (a,t) = 0\) for \(a \geq L\) and all \(t \geq 0\). In consequence, this implies that the function \(\lambda (a)\) must be singular at \(a = L\). We are concerned with the problem of determining the death function \(\lambda (a)\) or, as is more suitable to our formulation, the life table \(\pi\) from overposed data consisting of the values of the age-structure at a later time \(T\).
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 47N60
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 60J85
Mathematics Subject Classification ID: 47N30
zbMATH DE Number: 584081
zbMATH Keywords: inverse problem
zbMATH Keywords: ill-posedness
zbMATH Keywords: convergence of regularized solutions
zbMATH Keywords: operator equation
zbMATH Keywords: least squares
zbMATH Keywords: birth and death processes
zbMATH Keywords: age-structured populations
zbMATH Keywords: life table
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1112
OpenAlex ID: W2091785183
DOI: 10.1006/JMAA.1994.1112
description: scientific article; zbMATH DE number 584081