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arXiv · 2402.01747

Existence and Uniqueness of Weak Solutions to Frictionless-Antiplane Contact Problems

Besma Fadlia·Mohamed Dalah·Delfim F. M. Torres
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Abstract

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.

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Besma Fadlia, Mohamed Dalah, Delfim F. M. Torres. 2024-01-30. Existence and Uniqueness of Weak Solutions to Frictionless-Antiplane Contact Problems. https://doi.org/10.3390/math12030434

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