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$%Y. Kelanemer, Optimal control of fluid flow in soil 1. Deterministic case, Rev. Mat. Complut. 11 (1998), no. 2, 373401. %$

Optimal Control of Fluid Flow in Soil 1. Deterministic Case
Youcef KELANEMER
Department of Computer Science
University of the Federal Armed Forces Munich
d-85577 Neubiberg Germany

Received: June 10, 1997
Revised: January 11, 1997
ABSTRACT

We study the numerical aspect of the optimal control of problems governed by a linear elliptic partial differential equation (PDE). We consider here the gas flow in porous media. The observed variable is the flow field we want to maximize in a given part of the domain or its boundary. The control variable is the pressure at one part of the boundary or the discharges of some wells located in the interior of the domain. The objective functional is a balance between the norm of the flux in the observation region and the costs due to the control variables. We consider several geometric configurations of the control and the observation variables, and we make use of different objective functionals. We take advantage of the linearity of the flux w.r.t. the control variable to significantly reduce the computational effort and to deduce the optimal controls of wide class of objective functionals. In this paper we consider the deterministic case where the model parameters are given in the whole domain.

1991 Mathematics Subject Classification: 49J20, 35J25, 35Q35.