Abstract
We examine, in this paper, a class of contact problems in elastostatics concerned with the steady frictional sliding of a metallic body on a rigid foundation. On the contact surface we assume that friction is governed by a law of a nonlocal type. We state both the classical and the variational formulations of the problem and then consider their relationship. We list two other related friction problems that can be obtained from the nonlocal case. Finally we address the questions of existence and uniqueness and show that under certain conditions (sufficiently small coefficient of friction or sufficiently large nonlocal parameter) the solution exists and is unique.
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