Existence of solutions of a thermoviscoplastic model and associated optimal control problems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Affiliation:	1. Technische Universität Chemnitz, Faculty of Mathematics, Professorship Numerical Mathematics (Partial Differential Equations), 09107 Chemnitz, Germany;2. Technische Universität Dortmund, Faculty of Mathematics, Lehrstuhl LSX, 44227 Dortmund, Germany;1. Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Lojasiewicza 6, 30348 Krakow, Poland;2. Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA;3. Federation University, Ballarat, Australia;1. Dipartimento di Matematica, Università deli Studi di Roma Sapienza, P.le Aldo Moro 5, 00185 Roma, Italy;2. Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli Federico II, Via Cintia, Monte S. Angelo, 80126 Napoli, Italy;1. Laboratoire de Mécanique, Physique et Modélisation Mathématique, Université de Médéa, Algeria;2. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;3. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania;1. Dpto. de Matemática Aplicada, Universidade de Santiago de Compostela, Campus Sur s/n, 15782 Santiago de Compostela, Spain;2. Dpto. de Estadística e Investigación Operativa, Universidade de Santiago de Compostela, Campus Sur s/n, 15782 Santiago de Compostela, Spain

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.

Keywords:	Thermoviscoplasticity Variational inequality of second kind Mixed boundary conditions Banach fixed-point theorem Maximal parabolic regularity Optimal control
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