Optimal control of quasistatic plasticity with linear kinematic hardening II: regularization and differentiability
type: Item
instance of: scholarly article
title: Optimal control of quasistatic plasticity with linear kinematic hardening II: regularization and differentiability
zbMATH Open document ID: 1342.49012
DOI: 10.4171/ZAA/1546
author: Gerd Wachsmuth
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2015-11-17T00:00:00Z
review text: Summary: We consider an optimal control problem governed by an evolution variational inequality arising in quasistatic plasticity with linear kinematic hardening. A regularization of the time-discrete problem is derived. The regularized forward problem can be interpreted as system of coupled quasilinear PDEs whose principal parts depend on the gradient of the state. We show the Fréchet differentiability of the solution map of this quasilinear system. As a consequence, we obtain a first order necessary optimality system. Moreover, we address certain convergence properties of the regularization. Editorial remark: for part I, see [Zbl 1258.49008].
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 49K21
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 74C05
zbMATH DE Number: 6510071
zbMATH Keywords: optimal control
zbMATH Keywords: evolution variational inequality
zbMATH Keywords: complementarity condition
zbMATH Keywords: quasistatic plasticity
zbMATH Keywords: regularization
zbMATH Keywords: Fréchet differentiability
zbMATH Keywords: necessary optimality system
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6510071