A class of differential hemivariational inequalities in Banach spaces

作者：Migorski, Stanislaw; Zeng, Shengda^*

来源：Journal of Global Optimization, 2018, 72(4): 761-779.

DOI：10.1007/s10898-018-0667-5

• Differential hemivariational inequality
• C-0-semigroup
• Rothe method
• Pseudomonotone
• Clarke subdifferential

In this paper we investigate an abstract system which consists of a hemivariational inequality of parabolic type combined with a nonlinear evolution equation in the framework of an evolution triple of spaces which is called a differential hemivariational inequality [(DHVI), for short]. A hybrid iterative system corresponding to (DHVI) is introduced by using a temporally semi-discrete method based on the backward Euler difference scheme, i.e., the Rothe method, and a feedback iterative technique. We apply a surjectivity result for pseudomonotone operators and properties of the Clarke subgradient operator to establish existence and a priori estimates for solutions to an approximate problem. Finally, through a limiting procedure for solutions of the hybrid iterative system, the solvability of (DHVI) is proved without imposing any convexity condition on the nonlinear function u bar right arrow f (t, x, u) and compactness of C-0-semigroup e(A(t)).

• 出版日期2018-12
• 单位北部湾大学