A class of fractional differential hemivariational inequalities with application to contact problem

作者：Zeng, Shengda^*; Liu, Zhenhai; Migorski, Stanislaw

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2018, 69(2): 36.

DOI：10.1007/s00033-018-0929-6

• Differential hemivariational inequality
• Rothe method
• Clarke generalized gradient
• Fractional Caputo derivative
• Adhesion
• Fractional Kelvin-Voigt constitutive law

In this paper, we study a class of generalized differential hemivariational inequalities of parabolic type involving the time fractional order derivative operator in Banach spaces. We use the Rothe method combined with surjectivity of multivalued pseudomonotone operators and properties of the Clarke generalized gradient to establish existence of solution to the abstract inequality. As an illustrative application, a frictional quasistatic contact problem for viscoelastic materials with adhesion is investigated, in which the friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals, and the constitutive relation is modeled by the fractional Kelvin-Voigt law.

• 出版日期2018-4
• 单位北部湾大学; 广西民族大学