The Analytical Study of Some Contact Problems with or without Friction

Abstract

The work carried out in this thesis is devoted to the mathematical study of some problems of contact mechanics with friction in a dynamic context with boundary conditions. Thermo­elasto­ viscoplastic, thermo­viscoelastic, and electro­viscoelastic constitutive laws are considered. For each problem, we derive a variational formulation and then establish existence and uniqueness re­ sults for a weak solution. The proofs are based on arguments of evolutionary variational inequalities, parabolic inequalities, differential equations, and a fixed point theorem.