A CLASS OF NONLINEAR THERMO-PIEZOELECTRIC CONTACT PROBLEM WITH COULOMB'S LAW: EXISTENCE, UNIQUENESS AND CONVERGENCE

doi:10.1007/s10473-026-0115-4

Acta mathematica scientia,Series B ›› 2026, Vol. 46 ›› Issue (1): 255-274.doi: 10.1007/s10473-026-0115-4

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A CLASS OF NONLINEAR THERMO-PIEZOELECTRIC CONTACT PROBLEM WITH COULOMB'S LAW: EXISTENCE, UNIQUENESS AND CONVERGENCE

Jinxia CEN^1,*, Abdelhadi HACHLAF²

1. School of Mathematical Sciences, and National Center for Applied Mathematics in Chongqin, Chongqing Normal University, Chongqin 401331, China;
2. Laboratory of Mathematics, Modeling and Automatic Systems, Cadi Ayyad University, Faculty of Sciences Semlalia, Marrakech

Received:2024-03-20 Revised:2025-04-14 Online:2026-01-25 Published:2026-05-22
Contact: * Jinxia CEN, E-mail: jinxcen@163.com
About author:Abdelhadi HACHLAF, E-mail: abdelhadi.hachlaf@gmail.com
Supported by:
Project for Outstanding Young Talents in Bagui of Guangxi, the Natural Science Foundation of Guangxi (2021GX-NSFFA196004, 2024GXNSFBA010337), the NSFC (12371312), and the Natural Science Foundation of Chongqing (CSTB2024NSCQ-JQX0033). The second author was supported by the Postdoctoral Fellowship Program of CPSF (GZC20241534), and the Startup Project of Postdoctoral Scientific Research of Zhejiang Normal University (ZC304023924).

Abstract

Abstract: 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.

Key words: thermo-piezoelectric material, Signorini's condition, mixed formulation, existence and convergence, penality method, finite element method

CLC Number:

35B10

Jinxia CEN^1,*, 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.

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A CLASS OF NONLINEAR THERMO-PIEZOELECTRIC CONTACT PROBLEM WITH COULOMB'S LAW: EXISTENCE, UNIQUENESS AND CONVERGENCE

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