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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. [email protected]
Oumar Traoré
Affiliation:
Département de Mathématiques, Université de Ouagadougou, B.P. 7021, Ouagadougou 03, Burkina Faso. [email protected]
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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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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