Optimal Control of a Viscous Two-Field Damage Model with FatigueArticle
Authors: Livia Betz 1,2,3
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Livia Betz
Motivated by fatigue damage models, this paper addresses optimal control problems governed by a non-smooth system featuring two non-differentiable mappings. This consists of a coupling between a doubly non-smooth history-dependent evolution and an elliptic PDE. After proving the directional differentiability of the associated solution mapping, an optimality system which is stronger than the one obtained by classical smoothening procedures is derived. If one of the non-differentiable mappings becomes smooth, the optimality conditions are of strong stationary type, i.e., equivalent to the primal necessary optimality condition.
Volume: Volume 4
Section: Original research articles
Published on: August 11, 2023
Accepted on: July 18, 2023
Submitted on: January 19, 2023
Keywords: [MATH]Mathematics [math], [MATH]Mathematics [math], [en] damage models with fatigue non-smooth optimization evolutionary VIs optimal control of PDEs history-dependence strong stationarity AMS subject classifications. 34G25 34K35 49J20 49J27 74R99, damage models with fatigue, non-smooth optimization, evolutionary VIs, optimal control of PDEs, history-dependence, strong stationarity AMS subject classifications. 34G25, 34K35, 49J20, 49J27, 74R99