Strong stationarity for the control of viscous history-dependent evolutionary VIs arising in applications

2023/02/28 by Livia Betz, Betz, Livia
Mathematics · Medicine · #34G25 #34K35 #49J40 #49K21 #74R99 #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2302.14385

openalex publication_date 2023/02/28 · openalex created_date 2023/03/03 · openalex updated_date 2026/07/28

Abstract

This paper addresses optimal control problems governed by history-dependent EVIs with viscosity. One of the prominent properties of the state system is its non-smooth nature, so that the application of standard adjoint calculus is excluded. We extend the results from [7] by showing that history-dependent EVIs with viscosity can be formulated as non-smooth ODEs in Hilbert space in a general setting. The Hadamard directional differentiability of the solution map is investigated. Based on previous results, this allows us to establish strong stationary conditions for two different viscous damage models with fatigue.

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