Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality

Abstract

This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality (SOEHVI) with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality (FOEHVI) for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.

Dynamic History-Dependent Hemivariational Inequalities Controlled by Evolution Equations with Application to Contact Mechanics

“…On the contrary, the notion of hemivariational inequality was introduced and investigated by Panagiotopoulos in 1983, see [33,34], through applying properties of the Clarke subgradient, defined for locally Lipschitz functions. As an effective mathematical tool, it has been used to describe many important problems arising in mechanics and engineering such as unilateral contact problems in nonlinear elasticity, thermoviscoelastic frictional contact problems, obstacles problems, etc., during the last thirty years, see [15,18,[21][22][23]27,29,31,32,[38][39][40]42,43].…”