Sectorial Approach of the Gradient Observability of the Hyperbolic Semilinear Systems Intern and Boundary Cases - Applied Mathematics

AM > Vol.7 No.12, July 2016

Sectorial Approach of the Gradient Observability of the Hyperbolic Semilinear Systems Intern and Boundary Cases ()

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DOI: 10.4236/am.2016.712117 1,230 Downloads 1,922 Views

Author(s)

Adil Khazari, Ali Boutoulout

Affiliation(s)

Laboratory of Modeling Analysis & Computer Science (MACS), Department of Mathematics and Computer Science, Faculty of Sciences, Moulay Ismail University, Meknes, Morocco.

ABSTRACT

The aim of this paper is to study the notion of the gradient observability on a subregion w of the evolution domain W and also we consider the case where the subregion of interest is a boundary part of the system evolution domain for the class of semilinear hyperbolic systems. We show, under some hypotheses, that the flux reconstruction is guaranteed by means of the sectorial approach combined with fixed point techniques. This leads to several interesting results which are performed through numerical examples and simulations.

KEYWORDS

Distributed Systems, Semilinear Hyperbolic Systems, Boundary Reconstruction, Regional Boundary Gradient Observability, Regional Gradient Observability, Gradient Observability, Fixed Point, Sectorial Operator

Share and Cite:

Khazari, A. and Boutoulout, A. (2016) Sectorial Approach of the Gradient Observability of the Hyperbolic Semilinear Systems Intern and Boundary Cases. Applied Mathematics, 7, 1326-1339. doi: 10.4236/am.2016.712117.

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