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.
Show me the PDF file (318 KB), TEX file for this article.
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El-Hassan Essoufi Univ. Hassan 1 Laboratory MISI 26000 Settat, Morocco email: e.h.essoufi@gmail.com |
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Mohammed Alaoui Univ. Hassan 1 Laboratory MISI 26000 Settat, Morocco email:alaoui_fsts@yahoo.fr |
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Mustapha Bouallala Univ. Hassan 1 Laboratory MISI 26000 Settat, Morocco email: bouallalamustaphaan@gmail.com |
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