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Variational analysis of a frictional contact problem for viscoelastic bodies. (English) Zbl 1002.74074

Summary: We consider a mathematical model which describes the bilateral frictional contact between a nonlinearly viscoelastic body and a rigid foundation. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results when the friction coefficient is small. The proofs are based on classical results on elliptic variational inequalities and fixed point arguments. We also study the continuous dependence of solution with respect to the friction coefficient.

MSC:

74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
74G20 Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
49J40 Variational inequalities
74D10 Nonlinear constitutive equations for materials with memory
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