Control problems governed by time-dependent maximal monotone operators
Laboratoire LMPA, Department of Mathematics, Jijel University, Algeria.
Received: 5 June 2015
Revised: 27 November 2015
Accepted: 22 December 2015
The paper concerns on an infinite dimensional Hilbert space, the existence and uniqueness of absolutely continuous solutions, for Lipschitz single-valued perturbations of evolution problems involving maximal-monotone operators. This result allows us to extend to optimal control problems associated with such equations, the relaxation theorems with Young measures proved recently in [S. Saïdi, L. Thibault and M.F. Yarou, Numer. Funct. Anal. Optim. 34 (2013) 1156–1186].
Mathematics Subject Classification: 34A60 / 49A52
Key words: Maximal monotone operators / optimal control / pseudo-distance / Lipschitz perturbation / absolutely continuous / Young measures
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