Regional Boundary Observability with Constraints of the Gradient

Hamid Bourray, Ali Boutoulout, Mohamed Baddi

Department of Mathematics and Computer science, Faculty of Science, University of Moulay Isma?l, Meknès, Morocco.

DOI: 10.4236/ica.2012.34037                

Abstract

The aim of this paper is to explore the concept of observability with constraints of the gradient for distributed parabolic system evolving in spatial domain Ω, and which the state gradient is to be observed only on a part of the boundary of the system evolution domain. It consists in the reconstruction of the initial state gradient which must be between two prescribed functions in a subregion Γ of Ω. Two necessary conditions are given. The first is formulated in terms of the subdifferential associated with a minimized functional, and the second uses the Lagrangian multiplier method. Nu-merical illustrations are given to show the efficiency of the second approach and lead to open questions.

Keywords

Distributed Systems; Parabolic Systems; Regional Observability with Constraints; Regional Reconstruction

Conflicts of Interest

The authors declare no conflicts of interest.

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