Steady-state solutions for a reaction-diffusion equation with Robin boundary conditions: Application to the control of dengue vectors

In this paper, we investigate an initial-boundary-value problem of a reaction-diffusion equation in a bounded domain with a Robin boundary condition and introduce some particular parameters to consider the non-zero flux on the boundary. This problem arises in the study of mosquito populations under the intervention of the population replacement method, where the boundary condition takes into account the inflow and outflow of individuals through the boundary. Using phase-plane analysis, the present paper studies the existence and properties of non-constant steady-state solutions depending on several parameters. Then, we use the principle of linearized stability to prove some sufficient conditions for their stability. We show that the long-time efficiency of this control method depends strongly on the size of the treated zone and the migration rate. To illustrate these theoretical results, we provide some numerical simulations in the framework of mosquito population control.

Mots clés

Reaction-diffusion equations steady-state solutions robin boundary conditions

Domaines

Equations aux dérivées partielles [math.AP]

Fichier principal

preprint2.pdf (2.73 Mo)

F.png (188.39 Ko)

e001.png (121.15 Ko)

e005.png (130.63 Ko)

e01.png (131.52 Ko)

eu.png (17.27 Ko)

f.png (254.88 Ko)

fig0.png (126.47 Ko)

fig00.png (56.38 Ko)

fig01.png (55.95 Ko)

fig02.png (99.4 Ko)

fig03.png (80.34 Ko)

fig04.png (49.56 Ko)

fig1.png (69.63 Ko)

fig2.png (201.91 Ko)

fig3.png (116.55 Ko)

fig4.png (63.86 Ko)

fignonsym.png (20.19 Ko)

fignonsym0.png (29.37 Ko)

old_fig2.png (18.45 Ko)

p1.png (215.54 Ko)

p2.png (218.97 Ko)

pext01.png (121.65 Ko)

pext08.png (109.5 Ko)

pext082.png (85.07 Ko)

phase1.png (410.58 Ko)

phase2.png (454.42 Ko)

Origine	Fichiers produits par l'(les) auteur(s)

Origine	Fichiers produits par l'(les) auteur(s)

Nga Nguyen : Connectez-vous pour contacter le contributeur

https://hal.science/hal-03775887

Soumis le : lundi 25 septembre 2023-14:46:15

Dernière modification le : vendredi 8 novembre 2024-15:36:02

Dates et versions

hal-03775887 , version 1 (14-09-2022)

hal-03775887 , version 2 (25-09-2023)

Licence

Paternité

Identifiants

HAL Id : hal-03775887 , version 2
ARXIV : 2209.07165
DOI : 10.1017/S0956792523000256

Citer

Luís Almeida, Pierre-Alexandre Bliman, Nga Nguyen, Nicolas Vauchelet. Steady-state solutions for a reaction-diffusion equation with Robin boundary conditions: Application to the control of dengue vectors. European Journal of Applied Mathematics, 2023, 35 (3), pp.382-408. ⟨10.1017/S0956792523000256⟩. ⟨hal-03775887v2⟩

Exporter

BibTeX XML-TEI Dublin Core DC Terms EndNote DataCite

Collections

UNIV-PARIS13 ENS-PARIS UNIV-PARIS8 CNRS INRIA LAGA INSMI LJLL INRIA2 TDS-MACS PSL SORBONNE-UNIVERSITE SU-SCIENCES UNIV-PARIS-LUMIERES SORBONNE-PARIS-NORD UP-SCIENCES UNIV-PARIS8-OA ACT-R

291 Consultations

147 Téléchargements