J. Nonl. Evol. Equ. Appl. 2014 (4), pp. 37-52, published on December 23, 2014:

Cauchy System for an Hyperbolic Operator

M. Barry, G. B. Ndiaye

Département de Mathématiques-Informatique, Université Cheikh Anta Diop, Dakar; BP 5005, Sénégal

Received on January 19, 2014; Revised version on October 2, 2014
Accepted on October 2, 2014

Communicated by Gisèle Mophou

Abstract.  This paper deals with a control problem of a Cauchy System for an hyperbolic operator.The associate system here which is distributed and singular has in general no solution, and when a solution does exist it is unstable. So instead of considering the control v and the state z separately, we consider the pair control-state (v, z); it suffices then to make sure that the set of admissible pairs (v, z) is non-empty. We establish the existence and the uniqueness of the optimal pair and then we characterize it by using the penalization method.
Keywords:Singular Distributed System, Cauchy System for an hyperbolic operator, Admissible pair, Penalization, Singular Optimal System.
2010 Mathematics Subject Classification:   35-XX; 35LXX; 35L04.

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