Perturbed First Order State Dependent Moreau's Sweeping Process

Document Type : Research Paper


1 LMPA Laboratory, Department of Mathematics, Faculty of exact sciences ans computer sciences, MSBY University, Jijel, Algeria

2 LMPA Laboratory, Department of Mathematics, Faculty of Exact Sciences and Computer Science, MSBY University, Jijel, Algeria


In this paper, we deal with the state-dependent nonconvex sweeping process motivated through quasi-variational inequalities arising in the evolution of sandpiles, quasistatic evolution problems with friction, micromechanical damage models for iron materials. We prove the existence of absolutely continuous solution for the problem in presence of a perturbation, that is an external force applied on the system. The perturbation considered here is general and take the form of a sum of a single-valued Carath'eodory mapping and a set-valued unbounded mapping.