无摩擦-反平面接触问题弱解的存在性与唯一性
Existence and Uniqueness of Weak Solutions to Frictionless-Antiplane Contact Problems
AI总结：
本文研究准静态-反平面接触问题，针对热-电-粘弹性材料，通过变分公式化（含半变分不等式、椭圆和抛物方程），证明了模型弱解的存在性与唯一性。
摘要：
我们研究了一个准静态-反平面接触问题，考察一种具有依赖于滑移率的摩擦定律的热-电-粘弹性材料，并假设基础是导电的。该力学问题由偏微分方程组表示，建立其解涉及几个关键步骤。首先，我们获得模型的变分公式化，该公式包含三个系统：一个半变分不等式、一个椭圆方程和一个抛物方程。随后，我们证明了模型存在唯一的弱解。证明依赖于多种论证，包括与演化不等式相关的论证、解耦未知数的技术以及微分方程的某些结果。
英文摘要：
We investigate a quasi-static-antiplane contact problem, examining a thermo-electro-visco-elastic material with a friction law dependent on the slip rate, assuming that the foundation is electrically conductive. The mechanical problem is represented by a system of partial differential equations, and establishing its solution involves several key steps. Initially, we obtain a variational formulation of the model, which comprises three systems: a hemivariational inequality, an elliptic equation, and a parabolic equation. Subsequently, we demonstrate the existence of a unique weak solution to the model. The proof relies on various arguments, including those related to evolutionary inequalities, techniques for decoupling unknowns, and certain results from differential equations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
