两个二维弹性杆的脱粘模型分析

Fixed Point Theory and Applications Pub Date : 2022-06-06 DOI:10.1186/s13663-022-00725-8

Shillor, Meir, Kuttler, Kenneth L.

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摘要

这项工作建立了一个由湿度和振动引起的两个弹性2d杆的脱粘过程的新模型的弱解的存在性。该模型的一个版本首次在波兰克拉科夫举行的PCM-CMM-2019会议上提出，并发表在《J. Theor》杂志上。达成。机械学报，58(2):295-305 2020)。通过对问题进行正则化，然后将其化为允许使用伪微分算子和不动点定理工具的抽象形式，证明了弱解的存在性。进一步分析解决方案、有效的数值方法和模拟以及可能的控制等问题尚未解决。

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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Analysis of a debonding model of two elastic 2D-bars

This work establishes the existence of a weak solution to a new model for the process of debonding of two elastic 2D-bars caused by humidity and vibrations. A version of the model was first presented in the PCM-CMM-2019 conference in Krakow, Poland, and was published in (Shillor in J. Theor. Appl. Mech. 58(2): 295–305 2020). The existence of a weak solution is proved by regularizing the problem and then setting it in an abstract form that allows the use of tools for pseudo-differential operators and a fixed point theorem. Questions of further analysis of the solutions, effective numerical methods and simulations, as well as possible controls, are unresolved, yet.

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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.