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

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.
Comment: This is a preprint of a paper whose final and definite form is published Open Access in 'Mathematics', at [https://doi.org/10.3390/math12030434]. Cite this paper as: Fadlia, B.; Dalah, M.; Torres, D.F.M. Existence and Uniqueness of Weak Solutions to Frictionless-Antiplane Contact Problems. Mathematics 12 (2024), no. 3, Art. 434