In this paper, we study a comprehensive mathematical model describing the problem of frictional contact between a nonlinear thermo-piezoelectric body and a rigid foundation with electrically conductive effect, in which the contact conditions are described by a Signorini's condition and Coulomb's friction law. We derive the variational form of the contact problem which is a mixed system formulated by variational inequalities and equalities. Then, we use standard results on mixed problems and the Banach fixed-point theorem to prove the existence and uniqueness of the solution to the contact problem. Moreover, we demonstrate the convergence of a penalty method for this contact problem under consideration. Finally, finite element method is applied to the penalty contact problem and a strong convergence theorem is obtained.
Jinxia CEN1
,
*
,
Abdelhadi HACHLAF2
. A CLASS OF NONLINEAR THERMO-PIEZOELECTRIC CONTACT PROBLEM WITH COULOMB'S LAW: EXISTENCE, UNIQUENESS AND CONVERGENCE[J]. Acta mathematica scientia, Series B, 2026
, 46(1)
: 255
-274
.
DOI: 10.1007/s10473-026-0115-4
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