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

top
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

top

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/221912>.

@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; heat equation; Kakutani-Fan-Glicksberg fixed point theorem},
language = {eng},
month = {11},
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/221912},
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
DA - 2011/11//
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; heat equation; Kakutani-Fan-Glicksberg fixed point theorem
UR - http://eudml.org/doc/221912
ER -

References

top
  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 I323 (1996) 269–274.  Zbl0874.93054
  2. S. Anita, Analysis and control of age-dependent population dynamics . Kluwer Academic Publishers (2000).  Zbl0960.92026
  3. J.P. Aubin, L'analyse non linéaire et ses motivations économiques . Masson, Paris (1984).  
  4. V. Barbu, M. Ianneli and M Martcheva, On the controllability of the Lotka-McKendrick model of population dynamics. J. Math. Anal. Appl.253 (2001) 142–165.  Zbl0961.92024
  5. O. Kavian and L. de Teresa, Unique continuation principle for systems of parabolic equations. ESAIM: COCV16 (2010) 247–274.  Zbl1195.35080
  6. M. Langlais, A nonlinear problem in age-dependent population diffusion. SIAM J. Math. Anal.16 (1985) 510–529.  Zbl0589.92013
  7. F.H. Lin, A uniqueness theorem for parabolic equation. Com. Pure Appl. Math.XLII (1990) 123–136.  
  8. A. Ouédraogo and O. Traoré, Sur un problème de dynamique des populations. IMHOTEP J. Afr. Math. Pures Appl.4 (2003) 15–23.  
  9. A. Ouédraogo and O. Traoré, Optimal control for a nonlinear population dynamics problem. Port. Math. (N.S.)62 (2005) 217–229.  Zbl1082.92038
  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.  Zbl1227.93088
  11. E. Zeidler, Nonlinear functional analysis and its applications, Applications to Mathematical PhysicsIV. Springer-Verlag, New York (1988).  Zbl0648.47036
  12. E. Zuazua, Finite dimensional null controllability of the semilinear heat equation. J. Math. Pures Appl.76 (1997) 237–264.  Zbl0872.93014

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.