Existence of Solutions for Sweeping Processes with Local Conditions

Sweeping processes, introduced by J. J. Moreau, have been studied significantly in recent years due to their interesting applications in practice. However, most of the researches use the global Hausdorff distance to describe the movement of the moving set, which is probably not satisfied for unbounded cases. In this paper, we study the existence of solutions for sweeping processes by using only local excess condition. The result obtained can be applied to analyze a class of time-varying evolution variational inequalities.