A Class of time-fractional hemivariational inequalities with application to frictional contact problem

作者：Zeng Shengda; Migorski Stanislaw

来源：Communications in Nonlinear Science & Numerical Simulation, 2018, 56: 34-48.

DOI：10.1016/j.cnsns.2017.07.016

• Hemivariational inequality
• Rothe method
• Clarke subdifferential
• Caputo derivative
• Fractional viscoelastic constitutive law
• Friction

In this paper a class of elliptic hemivariational inequalities involving the time-fractional order integral operator is investigated. Exploiting the Rothe method and using the surjectivity of multivalued pseudomonotone operators, a result on existence of solution to the problem is established. Then, this abstract result is applied to provide a theorem on the weak solvability of a fractional viscoelastic contact problem. The process is quasistatic and the constitutive relation is modeled with the fractional Kelvin–Voigt law. The friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals. The variational formulation of this problem leads to a fractional hemivariational inequality.

• 出版日期2018-3