A Class of time-fractional hemivariational inequalities with application to frictional contact problem
A Class of time-fractional hemivariational inequalities with application to frictional contact problem
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DOI：
10.1016/j.cnsns.2017.07.016
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发表时间：
2018-03
期刊：
影响因子：
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通讯作者：
Shengda Zeng;S. Migórski
中科院分区：
文献类型：
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作者：
Shengda Zeng;S. Migórski
本文研究了一类涉及时间分数阶积分算子的椭圆型半变分不等式。利用Rothe方法和多值伪单调算子的满射性，建立了该问题解的存在性的一个结果。然后，应用这一抽象结果给出了分数阶粘弹性接触问题弱解的一个定理。该过程是准静态的，本构关系用分数Kelvin-Voigt定律来描述。摩擦接触条件用非凸非光滑泛函的Clarke广义梯度来描述。这个问题的变分形式导致了一个分数次半变分不等式。
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.