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E. Zerrik and H. Bourray, “Gradient Observability for Diffusion Systems,” International Journal of Applied Mathematics and Computer Science, Vol. 13, No. 2, 2003, pp. 39-50.

has been cited by the following article:

• TITLE: Regional Boundary Observability with Constraints of the Gradient

  AUTHORS: Hamid Bourray, Ali Boutoulout, Mohamed Baddi

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

  JOURNAL NAME: Intelligent Control and Automation, Vol.3 No.4, November 28, 2012

  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.