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

Author

Listed:
  • 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
    Faculty of Business and Communications, INTI International University, Persiaran Perdana BBN, Putra Nilai, Nilai 71800, Negeri Sembilan, Malaysia)

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.

Suggested Citation

  • Besma Fadlia & Mohamed Dalah & Delfim F. M. Torres, 2024. "Existence and Uniqueness of Weak Solutions to Frictionless-Antiplane Contact Problems," Mathematics, MDPI, vol. 12(3), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:434-:d:1329066
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