Boundary Constrained observability for hyperbolic systems

Adil Khazari; Fatima Ezzahrae El Alaoui; Ali Boutoulout

Adil Khazari National School of Commerce and Management, Sidi Mohamed Ben Abdellah University, Fez, Morocco.
Fatima Ezzahrae El Alaoui MACS Laboratory, Department of Mathematics, Moulay Ismail University, Faculty of Sciences, Meknes, Morocco.
Ali Boutoulout MACS Laboratory FS Moulay Ismail University

Abstract

The purpose of this paper is to introduce the concept of observability for distributed hyperbolic systems evolving in spatial domain $\omega$. It consists of the reconstruction of the initial conditions, on a subregion $\Gamma$ of $\partial\Omega$ , that the initial state and speed are to be observed between two prescribed functions given only on a boundary subregion $\Gamma$ . We give some denitions and properties of this kind of observability and we describe two approaches to solve this problem which the first is based on subdierential techniques and the second one uses the Lagrangian multiplier method. This last approach leads to an algorithm which is implemented numerically and illustrated through an example and simulation.