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SPDEs with space interactions and application to population modelling
Univ Biskra, Dept Math, Biskra, Algeria..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-1662-0215
Linnaeus Univ LNU, Dept Math, Växjö, Sweden..
Univ Oslo, Dept Math, Oslo, Norway..
2023 (English)In: ESAIM: Control, Optimisation and Calculus of Variations , ISSN 1292-8119, E-ISSN 1262-3377, Vol. 29, article id 18Article in journal (Refereed) Published
Abstract [en]

We consider optimal control of a new type of non-local stochastic partial differential equations (SPDEs). The SPDEs have space interactions, in the sense that the dynamics of the system at time t and position in space x also depend on the space-mean of values at neighbouring points. This is a model with many applications, e.g. to population growth studies and epidemiology. We prove the existence and uniqueness of strong, smooth solutions of a class of SPDEs with space interactions, and we show that, under some conditions, the solutions are positive for all times if the initial values are. Sufficient and necessary maximum principles for the optimal control of such systems are derived. Finally, we apply the results to study an optimal vaccine strategy problem for an epidemic by modelling the population density as a space-mean stochastic reaction-diffusion equation.

Place, publisher, year, edition, pages
EDP Sciences , 2023. Vol. 29, article id 18
Keywords [en]
Stochastic partial differential equations (SPDEs), strong, smooth solutions, space interactions, spacemean dependence, population modelling, maximum principle, backward stochastic partial differential equations (BSPDEs), space-mean stochastic reaction diffusion equation, optimal vaccination strategy
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-325243DOI: 10.1051/cocv/2023010ISI: 000942919500001Scopus ID: 2-s2.0-85149676992OAI: oai:DiVA.org:kth-325243DiVA, id: diva2:1748750
Note

QC 20230404

Available from: 2023-04-04 Created: 2023-04-04 Last updated: 2023-08-24Bibliographically approved

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Agram, Nacira

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CiteExportLink to record
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