Optimal Control for a Groundwater Pollution Ruled by a Convection–Diffusion–Reaction Problem

Autor: Eloïse Comte, Catherine Choquet, Emmanuelle Augeraud-Véron
Přispěvatelé: Université de La Rochelle (ULR), Mathématiques, Image et Applications - EA 3165 (MIA), Groupe de Recherche en Economie Théorique et Appliquée (GREThA), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2016
Předmět:
0209 industrial biotechnology
Mathematical optimization
Control and Optimization
Aquifer
02 engineering and technology
Management Science and Operations Research
01 natural sciences
020901 industrial engineering & automation
Groundwater pollution
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Nonlinearly coupled problem
Boundary value problem
Optimal control problem
[MATH]Mathematics [math]
0101 mathematics
Global existence
Mathematics
geography
geography.geographical_feature_category
Hydrogeology
[QFIN]Quantitative Finance [q-fin]
Fixed point theorem
Applied Mathematics
010102 general mathematics
Hydrogeological state equations
Optimal control problem
Hydrogeological state equations
Nonlinearly coupled problem
Parabolic and elliptic PDEs
Global existence
Fixed point theorem
Optimal control
Parabolic partial differential equation
6. Clean water
Controllability
13. Climate action
Parabolic and elliptic PDEs
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Convection–diffusion equation
Zdroj: Journal of Optimization Theory and Applications
Journal of Optimization Theory and Applications, Springer Verlag, 2016, 173 (3), pp.941-966. ⟨10.1007/s10957-016-1017-8⟩
Journal of Optimization Theory and Applications, Springer Verlag, In press, 173 (3), pp.941-966
Journal of Optimization Theory and Applications, Springer Verlag, 2016, ⟨10.1007/s10957-016-1017-8⟩
ISSN: 1573-2878
0022-3239
DOI: 10.1007/s10957-016-1017-8
Popis: International audience; We consider an optimal control problem of underground water contaminated by agricultural pollution. The economical intertemporal objective takes into account the trade-off between fertilizer use and cleaning costs. It is constrained by a hydrogeological model for the spread of the pollution in the aquifer. This model consists in a parabolic partial differential equation which is nonlinearly coupled through the dispersion tensor with an elliptic equation, in a three-dimensional domain. We prove the existence of a global optimal solution under various regularity assumptions and for a wide variety of boundary conditions. We also provide an asymptotic controllability result.
Databáze: OpenAIRE
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