A time-dependent obstacle problem in linearised elasticity. (March 2020)

• Record Type: Journal Article
• Authors: Piersanti, Paolo
• Is Part Of: Nonlinear analysis. Volume 192(2020)
• Publication Date: 2020-03
• Subjects: 35L04 -- 35L10 -- 35Q74 -- 35Q92; Obstacle problem -- Time-dependent -- Penalty method -- Variational inequalities -- Linearised elasticity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111660
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we establish the existence of solutions to a time-dependent problem for a linearly elastic body subjected to a confinement condition, expressing that all the points of the deformed reference configuration remain confined in a prescribed half space. This problem takes the form of a set of hyperbolic variational inequalities. The fact that any solution of the studied problem takes the form of a vector field instead of a real-valued function, the generality of the confinement condition under consideration, the fact that the integration domain is a subset of R 3, and the choice of the function space where solutions are sought make the analysis substantially more complicated, thus requiring the adoption of new resolution strategies.