L. Betz†
Abstract: This paper addresses optimal control problems governed by historydependent EVIs with viscosity. One of the prominent properties of the state system is its nonsmooth nature, so that the application of standard adjoint calculus is excluded. We extend previous results by showing that history-dependent EVIs with viscosity can be formulated as nonsmooth ODEs in Hilbert space in a general setting. The Hadamard directional di erentiability of the solution map is then investigated. This allows us to establish strong stationary conditions for two di erent viscous damage models with fatigue.
MSC: 34G25, 34K35, 49J40, 49K21, 74R99.
keywords: history-dependence, evolutionary VIs with viscosity, nonsmooth optimization, strong stationarity, fatigue, viscous damage evolution.
DOI 10.56082/annalsarscimath.2023.1-2.250
†livia.betz@uni-wuerzburg.de Faculty of Mathematics, University of Wurzburg, Emil-Fischer-Str.30, 97074 Wurzburg, Germany; Paper written with nancial support of the German Research Foundation under the DFG grant BE 7178/3-1.
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 15 no 1-2, 2023
