Regional Controllability of Semi-Linear Distributed Parabolic Systems: Theory and Simulation

Asmae Kamal, Ali Boutoulout, Sidi Ahmed Ould Beinane

Department of Mathematics, Al Jouf University, College of Sciences, Sakakah, Kingdom of Saudi Arabia.
TSI Group, Department of Mathematics and Computer Sciences, Moulay Ismail University, Faculty of Sciences, Meknes, Morocco.

DOI: 10.4236/ica.2012.32017                

Abstract

The aim of this brief paper is to give several results concerning the regional controllability of distributed systems governed by semi-linear parabolic equations. We concentrate on the determination of a control achieving internal and boundary regional controllability. The approach is based on an extension of the Hilbert Uniqueness Method (HUM) and Schauder’s fixed point theorem. We give a numerical example developed in internal and boundary sub region. These numerical illustrations show the efficiency of the approach and lead to conjectures.

Keywords

Semi-Linear Parabolic Systems; Regional; Internal/Boundary Controllability; Fixed-Point Theorems; Distributed System; HUM Approach

Conflicts of Interest

The authors declare no conflicts of interest.

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