Generalized Penalty and Regularization Method for Differential Variational-Hemivariational Inequalities

The primary objective of this paper is to study a large class of di erential variational-hemivariational inequalities involving history-dependent operators and constraints in a Banach space. First, we establish a well-posedness result, which includes existence, uniqueness, and continuous dependence on the initial data. Second, related penalized and regularized problems without constraints are introduced whose solutions approach the solution to the original inequality. Finally, these results are applied to an obstacle parabolic-elliptic system consisting of a nonlinear reaction-di usion equation and a time-dependent mixed boundary value problem with generalized gradient and Volterra integral terms.