Dynamic history-dependent variational-hemivariational inequalities with applications to contact mechanics

作者：Migorski Stanislaw; Ogorzaly Justyna^*

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2017, 68(1): 15.

DOI：10.1007/s00033-016-0758-4

• Variational-hemivariational inequality
• Clarke subdifferential
• Convex subdifferential
• History-dependent operator
• Viscoelastic material
• Frictional contact

In the paper we deliver a new existence and uniqueness result for a class of abstract nonlinear variational-hemivariational inequalities which are governed by two operators depending on the history of the solution, and include two nondifferentiable functionals, a convex and a nonconvex one. Then, we consider an initial boundary value problem which describes a model of evolution of a viscoelastic body in contact with a foundation. The contact process is assumed to be dynamic, and the friction is described by subdifferential boundary conditions. Both the constitutive law and the contact condition involve memory operators. As an application of the abstract theory, we provide a result on the unique weak solvability of the contact problem.

• 出版日期2017-2