Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-07-06T04:15:18.914Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximate controllability by birth control for 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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ainseba, B.E. and Langlais, M., Sur un problème de contrôle d'une population structurée en âge et en espace. C. R. Acad. Sci. Paris Série I 323 (1996) 269–274.
S. Anita, Analysis and control of age-dependent population dynamics . Kluwer Academic Publishers (2000).
J.P. Aubin, L'analyse non linéaire et ses motivations économiques . Masson, Paris (1984).
Barbu, V., Ianneli, M. and Martcheva, M, On the controllability of the Lotka-McKendrick model of population dynamics. J. Math. Anal. Appl. 253 (2001) 142–165. CrossRef
Kavian, O. and de Teresa, L., Unique continuation principle for systems of parabolic equations. ESAIM: COCV 16 (2010) 247–274. CrossRef
Langlais, M., A nonlinear problem in age-dependent population diffusion. SIAM J. Math. Anal. 16 (1985) 510–529. CrossRef
F.H. Lin, A uniqueness theorem for parabolic equation. Com. Pure Appl. Math. XLII (1990) 123–136.
Ouédraogo, A. and Traoré, O., Sur un problème de dynamique des populations. IMHOTEP J. Afr. Math. Pures Appl. 4 (2003) 15–23.
Ouédraogo, A. and Traoré, O., Optimal control for a nonlinear population dynamics problem. Port. Math. (N.S.) 62 (2005) 217–229.
Traoré, O., Approximate controllability and application to data assimilation problem for a linear population dynamics model. IAENG Int. J. Appl. Math. 37 (2007) 1–12.
E. Zeidler, Nonlinear functional analysis and its applications, Applications to Mathematical Physics IV. Springer-Verlag, New York (1988).
Zuazua, E., Finite dimensional null controllability of the semilinear heat equation. J. Math. Pures Appl. 76 (1997) 237–264. CrossRef