A fixed point result with applications in the study of viscoplastic frictionless contact problems
The paper studies a mathematical model which describes the frictionless contact between a viscoplastic body and a deformable foundation. The process is quasistatic and is studied on the general unbounded interval of time [0,1). First, the variational formulation of the problem is given. Then an abstract fixed point theorem is used in order to prove the existence of a unique weak solution to the model. The study contains in addition a regularity result. The techniques used in this paper are based on a recent monograph of the first author [\textit{W.\,Han} and \textit{M.\,Sofonea}, ``Quasistatic contact problems in viscoelasticity and viscoplasticity'' (AMS/IP Studies in Advanced Mathematics 30; Providence/RI:\ AMS International Press) (2002; Zbl 1013.74001)].
scientific article; zbMATH DE number 5289603