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

Besma Fadlia, Mohamed Dalah and Delfim F. M. Torres ()
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Besma Fadlia: Laboratory of Differential Equations, Department of Mathematics, University of Constantine 1, Ain El Bey Road, Constantine P.O. Box 325, Algeria
Mohamed Dalah: Laboratory of Applied Mathematics and Modeling, Department of Mathematics, University of Constantine 1, Ain El Bey Road, Constantine P.O. Box 325, Algeria
Delfim F. M. Torres: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Mathematics, 2024, vol. 12, issue 3, 1-14

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.

Keywords: electro-visco-elastic materials; antiplane problems; temperature fields; evolution variational inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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