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Regional Boundary Observability with Constraints: a Numerical Approach

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The aim of this paper is to develop the question of the boundary regional constrained observability for distributed parabolic system evolving in spatial domain Ω. It consists in the reconstruction of the initial position between two prescribed functions given only on a boundary subregion Г of . We give some definitions and properties of this concept and then we solve the problem of the reconstruction of the initial state using the Hilbert Uniqueness Method (HUM). This approach leads to an algorithm which is successfully implemented numerically and illustrated with examples and simulations.
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Distributed Systems; Parabolic Systems; Regional Constrained Observability; Boundary Reconstruction; HUM Approach

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