Optimization Problems for a thermoelastic frictional contact Problem

IF 1.6 3区 数学 Q1 MATHEMATICS
O. Baiz, H. Benaissa, R. Bouchantouf, D. E. Moutawakil
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引用次数: 2

Abstract

In the present paper, we analyze and study the control of a static thermoelastic contact problem. We consider a model which describes a frictional contact problem between a thermoelastic body and a deformable heat conductor obstacle. We derive a variational formulation of the model which is in the form of a coupled system of the quasi-variational inequality of elliptic type for the displacement and the nonlinear variational equation for the temperature. Then, under a smallness assumption, we prove the existence of a unique weak solution to the problem. Moreover, we establish the dependence of the solution with respect to the data and prove a convergence result. Finally, we introduce an optimization problem related to the contact model for which we prove the existence of a minimizer and provide a convergence result.
热弹性摩擦接触问题的优化问题
本文对静态热弹性接触问题的控制进行了分析和研究。我们考虑了一个描述热弹性体与可变形导热体障碍物之间摩擦接触问题的模型。我们推导了该模型的变分公式,其形式为位移的椭圆型拟变分不等式和温度的非线性变分方程的耦合系统。然后,在一个较小的假设下,我们证明了问题的唯一弱解的存在性。此外,我们还建立了解对数据的依赖关系,并证明了一个收敛结果。最后,我们引入了一个与接触模型相关的优化问题,并证明了最小化器的存在性并给出了收敛结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.80
自引率
5.60%
发文量
28
审稿时长
4.5 months
期刊介绍: Mathematical Modelling and Analysis publishes original research on all areas of mathematical modelling and analysis.
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