International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 49279, 20 pages
doi:10.1155/IJMMS/2006/49279
Null controllability of a nonlinear population dynamics problem
Département de Mathématiques, Université de Ouagadougou, Ouagadougou 03 BP 7021, Burkina Faso
Received 23 November 2005; Revised 8 August 2006; Accepted 11 October 2006
Copyright © 2006 Oumar Traore. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We establish a null controllability result for a nonlinear population dynamics model. In our model, the birth term is nonlocal and describes the recruitment process in newborn individuals population. Using a derivation of Leray-Schauder fixed point theorem and Carleman inequality for the adjoint system, we show that for all given initial density, there exists an internal control acting on a small open set of the domain and leading the population to extinction.