Glasnik Matematicki, Vol. 51, No. 2 (2016), 391-411.

ANALYSIS OF A SIGNORINI PROBLEM WITH NONLOCAL FRICTION IN THERMO-PIEZOELECTRICITY

H. Benaissa, EL-H. Essoufi and R. Fakhar

Univ Hassan 1, Laboratory MISI, 26000 Settat, Morocco
e-mail: e.h.essoufi@gmail.com

Univ Hassan 1, Laboratory LS3M, 25000 Khouribga, Morocco
e-mail: rfakhar@gmail.com

Abstract.   We consider a mathematical model which describes the frictional unilateral contact between a thermo-piezoelectric body and a rigid electrically conductive foundation. The thermo-piezoelectric constitutive law is assumed to be nonlinear and the contact is modeled with the Signorini condition, the nonlocal Coulomb friction law with slip dependent friction coefficient and the regularized electrical and thermal conductivity conditions. The variational form of this problem is a coupled system which consists of a nonlinear variational inequality for the displacement field and two nonlinear variational equations for the electric potential and the temperature. The existence of a unique weak solution to the problem is proved by using abstract results for elliptic variational inequalities and fixed point arguments.

2010 Mathematics Subject Classification.   35J85, 47J20, 49J40, 74F15, 74G30, 74M10, 74M15, 74S05.

Key words and phrases.   Static frictional contact, thermopiezoelectric material, Signorini conditions, Coulomb's friction, frictional heat generation, variational inequality, variational analysis, fixed point process.

DOI: 10.3336/gm.51.2.08

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