Abstract
The aim of this paper is to explore the concept of regional observability of the gradient for distributed hyperbolic systems evolving in spatial domain Ω and the reconstruction of the gradient of the system without the knowledge of the state. It consists in the reconstruction of the initial state gradient in a subregion ω of Ω. We give definitions and characterizations and some properties of this kind of regional observability, we also describe an approach to solve this problem, which is performed by numerical examples and simulation.
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