Existence of solutions of a thermoviscoplastic model and associated optimal control problems. (June 2017)

• Record Type: Journal Article
• Authors: Herzog, Roland; Meyer, Christian; Stötzner, Ailyn
• Is Part Of: Nonlinear analysis. Volume 35(2017)
• Page Start: 75
• Page End: 101
• Publication Date: 2017-06
• Subjects: Thermoviscoplasticity -- Variational inequality of second kind -- Mixed boundary conditions -- Banach fixed-point theorem -- Maximal parabolic regularity -- Optimal control; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.10.008
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: A quasistatic, thermoviscoplastic model at small strains with linear kinematic hardening, von Mises yield condition and mixed boundary conditions is considered. The existence of a unique weak solution is proved by means of a fixed-point argument, and by employing maximal parabolic regularity theory. The weak continuity of the solution operator is also shown. As an application, the existence of a global minimizer of a class of optimal control problems is proved. Highlights: We prove the existence of a unique weak solution of a thermoviscoplastic model. The model is fully coupled and it contains a variational inequality of second kind. We exploit an integrability result for nonl. elasticity and max. parabolic regularity. We formulate a class of opt. control problems and show existence of global minimizers. We show that the control-to-state operator is weakly sequentially continuous.