A class of time-dependent variational inequalities and their application in multi-layer contact systems

Based on the actual mechanical analysis of asphalt pavements, a class of multi-layer contact system problems with long memory terms and time-dependent interlayer contact conditions is proposed, and the corresponding time-dependent variational inequalities are further presented. Subsequently, based on general operator regularity assumptions, the existence, uniqueness, and regularity of the solutions to such variational inequalities over the unbounded time interval $R_{+}$, as well as the stability of the solutions to the contact system over a bounded time interval $I=[0,T]$, are analyzed. Finally, through numerical experiments, the influence of long memory terms and time-dependent contact conditions on the multi-layer contact system is further discussed and interpreted. The theoretical and numerical results collectively verify the feasibility and value of studying nonlinear phenomena in contact problems by formulating variational inequalities.