Existence of a solution to a dynamic unilateral contact problem for a cracked viscoelastic body

Existence of solutions for a dynamic Signorini's contact problem

“…(1)- (4). In order to prove that u verifies (5) we follow the work of Barral and Quintela [1] and finally, following similar techniques to those in Lions [9] we prove that u verifies the initial conditions (6).…”

“…Par exemple, Duvaut et Lions [5] ont considéré des problèmes de contact quasi-statiques et dynamiques avec frottement pour des milieux élastiques et viscoélastiques. Les problèmes de contact dynamiques pour des milieux viscoélastiques ont été étudiés par plusieurs autres auteurs : Martins et Oden [10] dans le cas de compliance normale ; Cocou [3] pour les conditions Signorini avec une loi de frottement non local ; Cocou et Scarella [4] ont étendu plus tard ce résultat à un milieu fissuré ; Jaruseck [6] pour un problème de contact sans frottement avec des conditions de Signorini pour un milieu avec une mémoire singulière.…”

“…For example, in [5], Duvaut and Lions have considered quasistatic and dynamic contact problems with given friction for linearly elastic and viscoelastic bodies. Dynamic contact problems involving viscoelastic bodies have been studied by several other authors: Martins and Oden [10] in the case of normal compliance; Cocou [3] for Signorini conditions and nonlocal friction; Cocou and Scarella [4] later extended this result to a cracked body; Jaruseck in [6] for Signorini frictionless contact problem for materials with a singular memory.…”

Analysis of a dynamic unilateral contact problem for a cracked viscoelastic body

“…M. Cocou [4] has obtained an existence result for a dynamic unilateral contact problem with nonlocal friction, for viscoelastic bodies of Kelvin-Voigt type, without any additional assumption on velocity or acceleration. In this paper, a similar technique is used to obtain an existence result for a cracked viscoelastic body (see also [6]). …”

Solvability of a class of thermal dynamical contact problems with subdifferential conditions

“…An early attempt at the study of contact problems for elastic viscoelastic materials within the mathematical analysis framework was introduced in the pioneering reference works [5,7,13,11,15]. More recently, the dynamic Signorini's problem for a cracked viscoelastic body is studied in [6]. Mathematical analysis of unilateral contact problems involving static, quasi-static and dynamic process may be found in the recent self-contained book [8].…”