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Global and regional constrained controllability for distributed parabolic linear systems: RHUM approach

  • * Corresponding author: Touria Karite

    * Corresponding author: Touria Karite 
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  • The aim of this paper is to study the problem of constrained controllability for distributed parabolic linear system evolving in spatial domain $ \Omega $ using the Reverse Hilbert Uniqueness Method (RHUM approach) introduced by Lions in 1988. It consists in finding the control $ u $ that steers the system from an initial state $ y_{_{0}} $ to a state between two prescribed functions. We give some definitions and properties concerning this concept and then we resolve the problem that relays on computing a control with minimum cost in the case of $ \omega = \Omega $ and in the regional case where $ \omega $ is a part of $ \Omega $.

    Mathematics Subject Classification: Primary: 93B05; 93C05; 93C20; Secondary: 34H05; 49J20.


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