Analysis of a dynamic viscoelastic unilateral contact problem with normal damped response. (April 2016)

• Record Type: Journal Article
• Authors: Han, Jiangfeng; Migórski, Stanisław; Zeng, Huidan
• Is Part Of: Nonlinear analysis. Volume 28(2016)
• Page Start: 229
• Page End: 250
• Publication Date: 2016-04
• Subjects: Dynamic -- Variational-hemivariational inequality -- Kelvin–Voigt law -- Clarke subdifferential -- Unique solvability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.10.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we deal with a viscoelastic unilateral contact problem with normal damped response. The process is assumed to be dynamic and frictionless. Normal damping function is modeled by the Clarke subdifferential of a nonconvex and nonsmooth function. First, the variational formulation of this problem is provided in the form of a nonlinear first order variational–hemivariational inequality for the velocity field. Then, based on the surjectivity results for pseudomonotone and maximal monotone operators, we obtain the unique solvability for a new class of abstract evolutionary variational-hemivariational inequalities. Finally, we apply our abstract results to prove the existence of a unique weak solution to the corresponding contact problem.