弹塑性障碍物上压电致动器的接触问题

Fixed Point Theory and Applications Pub Date : 2022-04-11 DOI:10.1186/s13663-022-00721-y

Krejčí, Pavel, Petrov, Adrien

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引用次数: 0

摘要

将压电致动器与弹塑性障碍物接触时的运动问题重新表述为具有体滞回和接触边界滞回的一维PDE问题。该模型耗散能量符合热力学原理。主要结果包括解的存在性、唯一性和连续数据依赖性。

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A contact problem for a piezoelectric actuator on an elasto-plastic obstacle

A problem of motion of a piezoelectric actuator in contact with an elasto-plastic obstacle is reformulated as a PDE in one spatial dimension with hysteresis in the bulk and on the contact boundary. The model is shown to dissipate energy in agreement with the principles of thermodynamics. The main result includes existence, uniqueness, and continuous data dependence of solutions.

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Fixed Point Theory and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： In a wide range of mathematical, computational, economical, modeling and engineering problems, the existence of a solution to a theoretical or real world problem is equivalent to the existence of a fixed point for a suitable map or operator. Fixed points are therefore of paramount importance in many areas of mathematics, sciences and engineering. The theory itself is a beautiful mixture of analysis (pure and applied), topology and geometry. Over the last 60 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in such diverse fields as biology, chemistry, physics, engineering, game theory and economics. In numerous cases finding the exact solution is not possible; hence it is necessary to develop appropriate algorithms to approximate the requested result. This is strongly related to control and optimization problems arising in the different sciences and in engineering problems. Many situations in the study of nonlinear equations, calculus of variations, partial differential equations, optimal control and inverse problems can be formulated in terms of fixed point problems or optimization.