A Long-Term Mathematical Model for Mining Industries
Achdou, Yves; Giraud, Pierre-Noël; Lasry, Jean-Michel; Lions, Pierre-Louis (2016), A Long-Term Mathematical Model for Mining Industries, Applied Mathematics and Optimization, 74, 3, p. 579–618. 10.1007/s00245-016-9390-0
TypeArticle accepté pour publication ou publié
Journal nameApplied Mathematics and Optimization
MetadataShow full item record
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Centre d'économie industrielle i3 [CERNA i3]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)A 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.
Subjects / KeywordsHeterogeneous agents model; Mean field games; Master equation; Hamilton Jacobi equations; Viscosity solution; Model calibration
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