Applied Mathematics & Information Sciences

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The aim of this paper is to develop the question of the regional constrained observability for distributed hyperbolic system evolving in spatial domain W. It consists in the reconstruction of the initial conditions, in a subregion w of W, knowing that the initial position is between two prescribed functions in w and also the initial speed is between two others functions also prescribed in w. We give some definitions and proprieties concerning this concept and then we describe two approaches for solving this problem. The first is based on subdifferential technics and the second uses the Lagrangian multiplier method. This last approach leads to an algorithm for the reconstruction of the initial conditions. The obtained results are illustrated by numerical simulations which lead to some conjectures.

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