Analysis of a piezoelectric contact problem with subdifferential boundary condition. Issue 5 (October 2014)

• Record Type: Journal Article
• Authors: Migórski, Stanisław; Ochal, Anna; Sofonea, Mircea
• Is Part Of: Proceedings. Volume 144:Issue 5(2014)
• Page Start: 1007
• Page End: 1025
• Publication Date: 2014-10
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210513000607
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : We consider a mathematical model which describes the frictionless contact between a piezoelectric body and a foundation. The contact process is quasi-static and the foundation is assumed to be insulated. The novelty of the model consists in the fact that the material behaviour is described with an electro-elastic–visco-plastic constitutive law and the contact is modelled with a subdifferential boundary condition. We derive a variational formulation of the problem which is in the form of a system coupling two nonlinear integral equations with a history-dependent hemivariational inequality and a time-dependent linear equation. We prove the existence of a weak solution to the problem and, under additional assumptions, its uniqueness. The proof is based on a recent result on history-dependent hemivariational inequalities obtained by Migórski, Ochal and Sofonea in 2011.