Variational inequalities represent an important class of nonlinear problems and occur in the mathematical description of a large variety of physical problems. The most recent method in the study of free boundary value problems arising in filtration, heat conduction and diffusion theory uses a reformulation of these problems as variational inequalities. Quite often these problems arise as controlled systems with specified objectives. Roughly speaking, optimal control is concerned with finding the optimal input controls, within prescribed restrictions, in order to achieve the desired objectives.

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