Approximate controllability by birth control for a nonlinear population dynamics model

Otared Kavian; Oumar Traoré

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 4, page 1198-1213
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Kavian, Otared, and Traoré, Oumar. "Approximate controllability by birth control for a nonlinear population dynamics model." ESAIM: Control, Optimisation and Calculus of Variations 17.4 (2011): 1198-1213. <http://eudml.org/doc/272751>.

@article{Kavian2011,
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.},
author = {Kavian, Otared, Traoré, Oumar},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {population dynamics; approximate controllability; characteristic lines; heat equation; fixed point theorem; nonlinear population dynamics model; unique continuation; Kakutani-Fan-Glicksberg fixed point theorem},
language = {eng},
number = {4},
pages = {1198-1213},
publisher = {EDP-Sciences},
title = {Approximate controllability by birth control for a nonlinear population dynamics model},
url = {http://eudml.org/doc/272751},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Kavian, Otared
AU - Traoré, Oumar
TI - Approximate controllability by birth control for a nonlinear population dynamics model
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2011
PB - EDP-Sciences
VL - 17
IS - 4
SP - 1198
EP - 1213
AB - 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.
LA - eng
KW - population dynamics; approximate controllability; characteristic lines; heat equation; fixed point theorem; nonlinear population dynamics model; unique continuation; Kakutani-Fan-Glicksberg fixed point theorem
UR - http://eudml.org/doc/272751
ER -

References

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  1. [1] B.E. Ainseba and M. Langlais, 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. Zbl0874.93054MR1404772
  2. [2] S. Anita, Analysis and control of age-dependent population dynamics . Kluwer Academic Publishers (2000). Zbl0960.92026MR1797596
  3. [3] J.P. Aubin, L'analyse non linéaire et ses motivations économiques . Masson, Paris (1984). Zbl0673.00015MR754997
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  5. [5] O. Kavian and L. de Teresa, Unique continuation principle for systems of parabolic equations. ESAIM: COCV 16 (2010) 247–274. Zbl1195.35080MR2654193
  6. [6] M. Langlais, A nonlinear problem in age-dependent population diffusion. SIAM J. Math. Anal.16 (1985) 510–529. Zbl0589.92013MR783977
  7. [7] F.H. Lin, A uniqueness theorem for parabolic equation. Com. Pure Appl. Math. XLII (1990) 123–136. Zbl0727.35063MR1024191
  8. [8] A. Ouédraogo and O. Traoré, Sur un problème de dynamique des populations. IMHOTEP J. Afr. Math. Pures Appl.4 (2003) 15–23. Zbl1286.92046MR2059066
  9. [9] A. Ouédraogo and O. Traoré, Optimal control for a nonlinear population dynamics problem. Port. Math. (N.S.) 62 (2005) 217–229. Zbl1082.92038MR2147450
  10. [10] O. Traoré, Approximate controllability and application to data assimilation problem for a linear population dynamics model. IAENG Int. J. Appl. Math.37 (2007) 1–12. Zbl1227.93088MR2384662
  11. [11] E. Zeidler, Nonlinear functional analysis and its applications, Applications to Mathematical Physics IV. Springer-Verlag, New York (1988). Zbl0648.47036MR932255
  12. [12] E. Zuazua, Finite dimensional null controllability of the semilinear heat equation. J. Math. Pures Appl.76 (1997) 237–264. Zbl0872.93014MR1441986

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