Abstract
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.
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Project supported by the National Science Center of Poland under Maestro Project No. UMO-2012/06/A/ST1/00262, National Science Center of Poland under Preludium Project No. 2017/25/N/ST1/00611, the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under Grant No. 3792/GGPJ/H2020/2017/0, NNSF of China Grant No. 11671101, Special Funds of Guangxi Distinguished Experts Construction Engineering.
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Zeng, S., Liu, Z. & Migorski, S. A class of fractional differential hemivariational inequalities with application to contact problem. Z. Angew. Math. Phys. 69, 36 (2018). https://doi.org/10.1007/s00033-018-0929-6
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DOI: https://doi.org/10.1007/s00033-018-0929-6
Keywords
- Differential hemivariational inequality
- Rothe method
- Clarke generalized gradient
- Fractional Caputo derivative
- Adhesion
- Fractional Kelvin–Voigt constitutive law