Abderrezak Kasri†
Abstract: This paper is devoted to study a quasistatic contact problem between a viscoelastic material with long memory and a foundation. The contact is modelled with a version of Coulombs law of dry friction and a general normal compliance condition. We derive a variational formulation of the model and, under a smallness assumption, we establish the existence of a weak solution to the problem. The proof is based on the time-discretization method, the Banach xed point theorem and arguments of compactness, lower semicontinuity and monotonicity.
MSC: 49J40, 74A20, 74A55, 74D05.
keywords: Viscoelastic materials, long memory, quasistatic process, Coulombs law of dry friction, normal compliance, the time-discretization method, lower semicontinuity, the Banach xed point theorem, variational inequalities.
DOI 10.56082/annalsarscimath.2021.1-2.142
†kariabdezak@gmail.com Departement de Mathematiques, Faculte des Sciences, Universite 20 Aout 1955- Skikda, B.P.26 Route El-Hadaiek Skikda-Algerie.
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 13 no 1-2, 2021
