On a class of population dynamics problem with mixed boundary conditions
type: Item
instance of: scholarly article
title: On a class of population dynamics problem with mixed boundary conditions
zbMATH Open document ID: 1211.37110
author: Krishnan Balachandran
author: R. Lakshmi Lavanya
published in: Acta Applicandae Mathematicae
publication date: 2010-12-03T00:00:00Z
review text: The paper deals with a linear model describing the dynamics of a single species population with age dependence and spatial structure. The equation is considered in a bounded domain in \({\mathbb R}^n\), having a regular boundary. The birth process is described by a nonlocal term and the diffusion of individuals in the domain follows a Fick's law. The main result of the paper concerns the null controllability for the model. The exact null controllability is proven by employing a Carleman inequality with mixed boundary conditions for the backward adjoint population dynamics problem. The proof of this estimate is obtained using a standard technique from the theory of abstract parabolic equations. It is shown that one can expect to compute the initial distribution of individuals using observations on a small part of the boundary.
reviewed by: Iulian Stoleriu
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 37N35
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5822860
zbMATH Keywords: Carleman estimate
zbMATH Keywords: observability
zbMATH Keywords: population dynamics
zbMATH Keywords: controllability
MaRDI profile type: Publication
full work available at URL: s10440-010-9572-8
OpenAlex ID: W1967812562
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DOI: 10.1007/S10440-010-9572-8
description: scientific article; zbMATH DE number 5822860