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History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics. (English) Zbl 1231.74065
Summary: We consider a class of subdifferential inclusions involving a history-dependent term for which we provide an existence and uniqueness result. The proof is based on arguments on pseudomonotone operators and fixed point. Then we specialize this result in the study of a class of history-dependent hemivariational inequalities. Such kind of problems arises in a large number of mathematical models which describe quasistatic processes of contact between a deformable body and an obstacle, the so-called foundation. To provide an example we consider a viscoelastic problem in which the frictional contact is modeled with subdifferential boundary conditions. We prove that this problem leads to a history-dependent hemivariational inequality in which the unknown is the velocity field. Then we apply our abstract result in order to prove the unique weak solvability of the corresponding contact problem.
MSC:
74D10Nonlinear constitutive equations (materials with memory)
74M15Contact (solid mechanics)
49J40Variational methods including variational inequalities
35J87Nonlinear elliptic unilateral problems; nonlinear elliptic variational inequalities
47J22Variational and other types of inclusions
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