In this paper we present a new method to solve differential inclusions in Hilbert spaces. This method is a Galerkin-like method where we approach the original problem by projecting the state into a n-dimensional Hilbert ...

We show that any semi-algebraic sweeping process admits piecewise absolutely continuous solutions (trajectories), and any such bounded trajectory must have finite length. Analogous results hold more generally for ...

This paper is devoted to the study of a perturbed differential inclusion governed by a sweeping process in a Hilbert space. The sweeping process is perturbed by a sum of a single-valued map satisfying a Lipschitz condition ...

We give a full characterization of nonsmooth Lyapunov pairs for perturbed sweeping processes under very general hypotheses. As a consequence, we provide an existence result and a criterion for weak invariance for perturbed ...

This dissertation aims to study differential inclusions related to normal cones driven by nonregular moving sets (subsmooth and positively α-far) on Hilbert spaces. Specially, we are interested in a particular variant ...

In this note, by solving a variational inequality at each iteration, we study the existence of solutions for a class of sweeping processes with velocity in the moving set, originally introduced in a recent paper (Adly et ...

In this paper, an existence and uniqueness result of a class of second-order sweeping processes, with velocity in the moving set under perturbation in infinite-dimensional Hilbert spaces, is studied by using an implicit ...

In this paper, we prove the convergence strongly pointwisely (up to a subsequence) of Moreau-Yosida regularization of perturbed state-dependent sweeping process with nonregular (subsmooth and positively alpha-far) sets in ...

In this paper, we introduce and study degenerate state-dependent sweeping processes with nonregular moving sets (subsmooth and positively alpha-far). Based on the Moreau-Yosida regularization, we prove the existence of ...

The aim of this paper is to prove existence results for a class of sweeping processes in Hilbert spaces by using the catching-up algorithm. These processes are governed by ball-compact non autonomous sets. Moreover, a full ...