J. Nonl. Evol. Equ. Appl. 2021 (8), pp. 153-171, published on April 30, 2022:

Optimal control for evolution problem of incomplete data

T. Tindano, S. Tao

Université Joseph KI-ZERBO, Département de Mathématiques, 03 BP 7021 Ouagadougou 03 Burkina Faso.

S. Sawadogo

Ecole Normale Supérieure, Département des sciences exactes, 01 BP 1757 Ouagadougou 01 Burkina Faso.

Received on November 13, 2021, revised version on December 17, 2021
Accepted on December 23, 2021

Communicated by Gisèle Mophou

Abstract.  In this work, we give a characterization of the control for ill-posed problems.We propose the regularization method which consists to improve the data in order to obtain a well-posed problems. Indeed, the optimal control of the regularized system is discussed and the approximated optimality system is presented. We go from the limit and we obtain a singular optimality system for the low-regret. We use the convergence of the low-regret control to the no-regret control for which we obtain a characterization of the control for the original problem.
Keywords:Low-regret, no-regret, regularization technique.
2010 Mathematics Subject Classification:   35Q93, 49J20, 93C05, 93C41.

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