Resource allocation in a PDE ecosystem model.
Habitat heterogeneity
Optimal control theory
Resource allocation
Spatial ecology
Journal
Journal of mathematical biology
ISSN: 1432-1416
Titre abrégé: J Math Biol
Pays: Germany
ID NLM: 7502105
Informations de publication
Date de publication:
22 05 2023
22 05 2023
Historique:
received:
01
06
2022
accepted:
03
05
2023
revised:
01
05
2023
medline:
24
5
2023
pubmed:
23
5
2023
entrez:
22
5
2023
Statut:
epublish
Résumé
The effects of habitat heterogeneity on a diffusing population are investigated here. We formulate a reaction-diffusion system of partial differential equations to analyze the effect of resource allocation in an ecosystem with resource having its own dynamics in space and time. We show a priori estimates to prove the existence of state solutions given a control. We formulate an optimal control problem of our ecosystem model such that the abundance of a single species is maximized while minimizing the cost of inflow resource allocation. In addition, we show the existence and uniqueness of the optimal control as well as the optimal control characterization. We also establish the existence of an optimal intermediate diffusion rate. Moreover, we illustrate several numerical simulations with Dirichlet and Neumann boundary conditions with the space domain in 1D and 2D.
Identifiants
pubmed: 37217639
doi: 10.1007/s00285-023-01932-6
pii: 10.1007/s00285-023-01932-6
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
96Informations de copyright
© 2023. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
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