Null controllability of a coupled model in population dynamics
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 i...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics of the Czech Academy of Science
2023-10-01
|
| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/148/3/mb148_3_4.pdf |
| _version_ | 1797744906835329024 |
|---|---|
| author | Younes Echarroudi |
| author_facet | Younes Echarroudi |
| author_sort | Younes Echarroudi |
| collection | DOAJ |
| description | 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.\looseness-2 |
| first_indexed | 2024-03-12T15:15:52Z |
| format | Article |
| id | doaj.art-51ec027a339948b88b1d198940107d19 |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-03-12T15:15:52Z |
| publishDate | 2023-10-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-51ec027a339948b88b1d198940107d192023-08-11T11:14:53ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362023-10-01148334940810.21136/MB.2022.0088-21MB.2022.0088-21Null controllability of a coupled model in population dynamicsYounes EcharroudiWe 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.\looseness-2http://mb.math.cas.cz/full/148/3/mb148_3_4.pdf degenerate population dynamics model lotka-volterra system carleman estimate observability inequality null controllability |
| spellingShingle | Younes Echarroudi Null controllability of a coupled model in population dynamics Mathematica Bohemica degenerate population dynamics model lotka-volterra system carleman estimate observability inequality null controllability |
| title | Null controllability of a coupled model in population dynamics |
| title_full | Null controllability of a coupled model in population dynamics |
| title_fullStr | Null controllability of a coupled model in population dynamics |
| title_full_unstemmed | Null controllability of a coupled model in population dynamics |
| title_short | Null controllability of a coupled model in population dynamics |
| title_sort | null controllability of a coupled model in population dynamics |
| topic | degenerate population dynamics model lotka-volterra system carleman estimate observability inequality null controllability |
| url | http://mb.math.cas.cz/full/148/3/mb148_3_4.pdf |
| work_keys_str_mv | AT younesecharroudi nullcontrollabilityofacoupledmodelinpopulationdynamics |