Null controllability of a coupled model in population dynamics

Younes Echarroudi

Mathematica Bohemica (2023)

  • Volume: 148, Issue: 3, page 349-408
  • ISSN: 0862-7959

Abstract

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We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the “gene type” of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed by one control force. To reach our goal, we develop first a Carleman type inequality for its adjoint system and consequently the pertinent observability inequality. Note that such a system is obtained via the original paradigm using the Lagrangian method. Afterwards, with the help of a cost function we will be able to deduce the existence of a control acting on a subset of the gene type domain and which steers both populations of a certain class of age to extinction in a finite time.

How to cite

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Echarroudi, Younes. "Null controllability of a coupled model in population dynamics." Mathematica Bohemica 148.3 (2023): 349-408. <http://eudml.org/doc/299118>.

@article{Echarroudi2023,
abstract = {We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the “gene type” of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed by one control force. To reach our goal, we develop first a Carleman type inequality for its adjoint system and consequently the pertinent observability inequality. Note that such a system is obtained via the original paradigm using the Lagrangian method. Afterwards, with the help of a cost function we will be able to deduce the existence of a control acting on a subset of the gene type domain and which steers both populations of a certain class of age to extinction in a finite time.},
author = {Echarroudi, Younes},
journal = {Mathematica Bohemica},
keywords = {degenerate population dynamics model; Lotka-Volterra system; Carleman estimate; observability inequality; null controllability},
language = {eng},
number = {3},
pages = {349-408},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Null controllability of a coupled model in population dynamics},
url = {http://eudml.org/doc/299118},
volume = {148},
year = {2023},
}

TY - JOUR
AU - Echarroudi, Younes
TI - Null controllability of a coupled model in population dynamics
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 3
SP - 349
EP - 408
AB - We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the “gene type” of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed by one control force. To reach our goal, we develop first a Carleman type inequality for its adjoint system and consequently the pertinent observability inequality. Note that such a system is obtained via the original paradigm using the Lagrangian method. Afterwards, with the help of a cost function we will be able to deduce the existence of a control acting on a subset of the gene type domain and which steers both populations of a certain class of age to extinction in a finite time.
LA - eng
KW - degenerate population dynamics model; Lotka-Volterra system; Carleman estimate; observability inequality; null controllability
UR - http://eudml.org/doc/299118
ER -

References

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