Electron. J. Differential Equations, Vol. 2019 (2019), No. 05, pp. 1-21.

Quasistatic thermo-electro-viscoelastic contact problem with Signorini and Tresca's friction

El-Hassan Essoufi, Mohammed Alaoui, Mustapha Bouallala

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.

Submitted August 14, 2017. Published January 10, 2019.
Math Subject Classifications: 74F15, 74M15, 74M10, 49J40, 37L65, 46B50.
Key Words: Thermo-piezo-electric; Tresca's friction; Signorini's condition; variational inequality; Banach fixed point; Faedo-Galerkin method; compactness method; penalty method.

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El-Hassan Essoufi
Univ. Hassan 1
Laboratory MISI
26000 Settat, Morocco
email: e.h.essoufi@gmail.com
Mohammed Alaoui
Univ. Hassan 1
Laboratory MISI
26000 Settat, Morocco
email:alaoui_fsts@yahoo.fr
Mustapha Bouallala
Univ. Hassan 1
Laboratory MISI
26000 Settat, Morocco
email: bouallalamustaphaan@gmail.com

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