Existence and convergence theorems for evolutionary hemivariational inequalities of second order

Abstract

This article concerns with a class of evolutionary hemivariational inequalities in the framework of evolution triple. Based on the Rothe method, monotonicity-compactness technique and the properties of Clarke's generalized derivative and gradient, the existence and convergence theorems to these problems are established. The main idea in the proof is using the time difference to construct the approximate problems. The work generalizes the existence results on evolution inclusions and hemivariational inequalities of second order.

Keywords

• Hemivariational inequality
• nonlinear evolution inclusion
• Rothe method
• pseudomonotone operator
• Clarke's generalized gradient