Meir Shillor, Mircea Sofonea and J. Joachim Telega,

A survey of recent mathematical models and results for quasistatic
processes of frictional or frictionless contact between a deformable
body and a rigid or flexible foundation is presented. The processes of wear,
adhesion and damage, which accompany most contact processes, are
taken into account in some of the models. In others, thermal effect
are included. The various contact boundary conditions which are the main
topics of Contact Mechanics are described in detail. For each
problem the classical model and its weak or variational formulation are
presented, and the statements of the relevant existence and uniqueness
results are provided. It is concluded that the Mathematical Theory of
Contact Mechanics has progressed considerably in the last decade and
is reaching maturity. However, many open problems and questions
remain to be resolved, some of which are described, too.