非单调边界条件下弹粘塑性动态接触问题的连续依赖与最优控制

IF 1.3 4区数学 Q1 MATHEMATICS

Evolution Equations and Control Theory Pub Date : 2022-01-01 DOI:10.3934/eect.2021064

Xilu Wang, Xiaoliang Cheng

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引用次数: 1

摘要

本文研究具有Clarke次微分边界条件的弹粘塑性动态接触模型的连续依赖和最优控制问题。由于弹粘塑性材料的本构律具有应力场的隐式表达式，因此该模型的弱形式是一个演化半变分不等式与积分方程耦合。通过提供一些等效的弱公式，证明了在弱拓扑中解对外力和初始条件的连续依赖。最后，建立了一类边界最优控制问题的最优解的存在性。

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Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.

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来源期刊

Evolution Equations and Control Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.10

自引率

6.70%

发文量

期刊介绍： EECT is primarily devoted to papers on analysis and control of infinite dimensional systems with emphasis on applications to PDE''s and FDEs. Topics include: * Modeling of physical systems as infinite-dimensional processes * Direct problems such as existence, regularity and well-posedness * Stability, long-time behavior and associated dynamical attractors * Indirect problems such as exact controllability, reachability theory and inverse problems * Optimization - including shape optimization - optimal control, game theory and calculus of variations * Well-posedness, stability and control of coupled systems with an interface. Free boundary problems and problems with moving interface(s) * Applications of the theory to physics, chemistry, engineering, economics, medicine and biology