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Approximate controllability by birth controlfor a nonlinear population dynamics model

Published online by Cambridge University Press:  02 December 2010

Otared Kavian  and
Oumar Traoré
Otared Kavian
Affiliation:
Département de Mathématiques & LMV (CNRS, UMR 8100); Université de Versailles-Saint-Quentin-en-Yvelines, 45 avenue des États-Unis, 78035 Versailles Cedex, France. kavian@math.uvsq.fr
Oumar Traoré
Affiliation:
Département de Mathématiques, Université de Ouagadougou, B.P. 7021, Ouagadougou 03, Burkina Faso. traore.oumar@univ-ouaga.bf
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Abstract

In this paper we analyse an approximate controllability result for a nonlinear population dynamics model. In this model the birth term is nonlocal and describes the recruitment process in newborn individuals population, and the control acts on a small open set of the domain and corresponds to an elimination or a supply of newborn individuals. In our proof we use a unique continuation property for the solution of the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem.

Keywords

Population dynamicsapproximate controllabilitycharacteristic linesHeat equationfixed point theorem
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 4 , October 2011 , pp. 1198 - 1213
Copyright
© EDP Sciences, SMAI, 2010

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