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dc.contributor.authorAchdou, Yves
dc.contributor.authorGiraud, Pierre-Noël
dc.contributor.authorLasry, Jean-Michel
dc.contributor.authorLions, Pierre-Louis
dc.date.accessioned2019-02-28T15:02:12Z
dc.date.available2019-02-28T15:02:12Z
dc.date.issued2016
dc.identifier.issn0095-4616
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18500
dc.language.isoenen
dc.subjectHeterogeneous agents modelen
dc.subjectMean field gamesen
dc.subjectMaster equationen
dc.subjectHamilton Jacobi equationsen
dc.subjectViscosity solutionen
dc.subjectModel calibrationen
dc.subject.ddc515en
dc.titleA Long-Term Mathematical Model for Mining Industriesen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenA parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimen-sionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton-Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.en
dc.relation.isversionofjnlnameApplied Mathematics and Optimization
dc.relation.isversionofjnlvol74en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2016-12
dc.relation.isversionofjnlpages579–618en
dc.relation.isversionofdoi10.1007/s00245-016-9390-0en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-02-28T14:55:26Z
hal.person.labIds542019
hal.person.labIds73831
hal.person.labIds60
hal.person.labIds4262


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