The aim of this paper, dealing with the management of fresh water, is to present an optimal control approach for the steady flow in a rectangular aquifer there are two wells. The classical problem is a free boundary problem. After a change of variable transformation, we obtain an optimal control problem in a fixed domain, where the control appears in a Dirichlet boundary condition and in the coefficients of the state equation. After a finite element discretization, we obtain an optimization problem where the cost function is differentiable and the gradient could be computed analytically.
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- Optimal Control Approach for a Flow in Unsaturated Porous Media
C. M. Murea
- Springer Netherlands