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 dynamics, approximate controllability, characteristic lines, heat equation, fixed point theorem
@article{COCV_2011__17_4_1198_0,
author = {Kavian, Otared and Traor\'e, Oumar},
title = {Approximate controllability by birth control for a nonlinear population dynamics model},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1198--1213},
year = {2011},
publisher = {EDP Sciences},
volume = {17},
number = {4},
doi = {10.1051/cocv/2010043},
mrnumber = {2859872},
zbl = {1236.93022},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2010043/}
}
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 SP - 1198 EP - 1213 VL - 17 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2010043/ DO - 10.1051/cocv/2010043 LA - en ID - COCV_2011__17_4_1198_0 ER -
%0 Journal Article %A Kavian, Otared %A Traoré, Oumar %T Approximate controllability by birth control for a nonlinear population dynamics model %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 1198-1213 %V 17 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2010043/ %R 10.1051/cocv/2010043 %G en %F COCV_2011__17_4_1198_0
Kavian, Otared; Traoré, Oumar. Approximate controllability by birth control for a nonlinear population dynamics model. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1198-1213. doi: 10.1051/cocv/2010043
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