Existence of solutions of a thermoviscoplastic model and associated optimal control problems. (June 2017) - Herzog, Roland; Meyer, Christian; Stötzner, Ailyn
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.