Quasistatic thermo-electro-viscoelastic contact problem with Signorini and Tresca's friction
Date
2019-01-10
Authors
Essoufi, El-Hassan
Alaoui, Mohammed
Bouallala, Mustapha
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we consider a mathematical model that describes the quasi-static process of contact between a thermo-electro-viscoelastic body and a conductive foundation. The constitutive law is assumed to be linear thermo-electro-elastic and the process is quasistatic. The contact is modelled with a Signiorini's condition and the friction with Tresca's law. The boundary conditions of the electric field and thermal conductivity are assumed to be non linear. First, we establish the existence and uniqueness result of the weak solution of the model. The proofs are based on arguments of time-dependent variational inequalities, Galerkin's method and fixed point theorem. Also we study a associated penalized problem. Then we prove its unique solvability as well as the convergence of its solution to the solution of the original problem, as the penalization parameter tends to zero.
Description
Keywords
Thermo-piezo-electric, Tresca's friction, Signorini's condition, Variational inequality, Banach fixed point, Faedo-Galerkin method, Compactness method, Penalty method
Citation
Essoufi, E. H., Alaoui, M., & Bouallala, M. (2019). Quasistatic thermo-electro-viscoelastic contact problem with Signorini and Tresca's friction. <i>Electronic Journal of Differential Equations, 2019</i>(05), pp. 1-21.
Rights
Attribution 4.0 International