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Sectorial Approach of the Gradient Observability of the Hyperbolic Semilinear Systems Intern and Boundary Cases
Laboratory of Modeling Analysis & Computer Science (MACS), Department of Mathematics and Computer Science, Faculty of Sciences, Moulay Ismail University, Meknes, Morocco
Laboratory of Modeling Analysis & Computer Science (MACS), Department of Mathematics and Computer Science, Faculty of Sciences, Moulay Ismail University, Meknes, Morocco
- 1 Laboratory of Modeling Analysis & Computer Science (MACS), Department of Mathematics and Computer Science, Faculty of Sciences, Moulay Ismail University, Meknes, Morocco
- 2 Laboratory of Modeling Analysis & Computer Science (MACS), Department of Mathematics and Computer Science, Faculty of Sciences, Moulay Ismail University, Meknes, Morocco
Applied Mathematics·Volume 07 (2016)·Pages 1326–1339·Published 25 July 2016·DOI10.4236/am.2016.712117
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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.
KeywordsDistributed SystemsSemilinear Hyperbolic SystemsBoundary ReconstructionRegional Boundary Gradient ObservabilityRegional Gradient ObservabilityGradient ObservabilityFixed PointSectorial Operator
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