Optimization problems for a viscoelastic frictional contact problem with unilateral constraints. (December 2019)

• Record Type: Journal Article
• Authors: Sofonea, Mircea; Xiao, Yi-bin; Couderc, Maxime
• Is Part Of: Nonlinear analysis. Volume 50(2019)
• Page Start: 86
• Page End: 103
• Publication Date: 2019-12
• Subjects: Viscoelastic material -- Frictional contact -- Unilateral constraint -- Weak solution -- Convergence results -- Optimization problems; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.04.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider a mathematical model which describes the contact between a viscoelastic body and a rigid-deformable foundation with memory effects. We derive a variational formulation of the model which is in the form of a history-dependent variational inequality for the displacement field. Then we prove the existence of a unique weak solution to the problem. We also study the continuous dependence of the solution with respect to the data and prove two convergence results, under different assumptions on the data. The proofs are based on arguments of lower semicontinuity, pseudomonotonicity, and compactness. Finally, we use our convergence results in the study of several optimization problems associated to the viscoelastic contact model.