Existence of solutions of a thermoviscoplastic model and associated optimal control problems

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• 作者：Roland Herzog^a ; ^{roland.herzog@mathematik.tu-chemnitz.de} ; Christian Meyer^b ; ^{cmeyer@math.tu-dortmund.de} ; Ailyn Stö ; tzner^a ; ^{ailyn.stoetzner@mathematik.tu-chemnitz.de}
• 关键词：Thermoviscoplasticity ; Variational inequality of second kind ; Mixed boundary conditions ; Banach fixed-point theorem ; Maximal parabolic regularity ; Optimal control
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：35
• 期：Complete
• 页码：75-101
• 全文大小：836 K
• 卷排序：35

文摘

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.