J. Nonl. Evol. Equ. Appl. 2021 (5), pp. 95-118, published on May 8, 2021:

Stackelberg control in an unbounded domain for a parabolic equation

L. L. Djomegne Njoukoue, G. Deugoue

University of Dschang, BP 67 Dschang, Cameroon, West region

Received on January 28, 2021, revised version on February 25, 2021
Accepted on March 5, 2021

Communicated by Gaston M. N'Guérékata

Abstract.  In this paper, we investigate the Stackelberg strategy for a parabolic equation in an unboundeddomain of RN , N ∈ N \ {0}. We assume that we can act on the system through two hierarchical controls. One control called follower which solves an optimal control problem while the other control named leader solves a null controllability problem. The results are obtained using appropriate observability inequality of Carleman and under the assumption that the uncontrolled region is bounded.
Keywords:Parabolic equation, Carleman inequality, Optimal control, Controllability, Stackelberg.
2010 Mathematics Subject Classification:   35K05; 35K55; 49J20; 93B05.

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