Abstract
Contact problems on the surface interaction of rigid stamps with a deformed layered medium are considered provided that the variable friction coefficients arise in the contact zone as a function of the coordinate under the horizontal motion of stamps. The cause of the variable friction coefficients arising may be surface phenomena induced by a complex rheology of the deformed-medium surface, the chemical reactions proceeding, or a change in the properties of the contact surface of the stamps, for example, as a result of the presence of separate particles of the wear contact surface of the stamp and the base.
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