A Class of Nonlinear Inclusions and Sweeping Processes in Solid Mechanics

We consider a new class of inclusions in Hilbert spaces for which we provide an existence and uniqueness result. The proof is based on arguments monotonicity, convexity fixed point. use this result to establish the unique solvability associated Moreau’s sweeping processes. Next, give two applications Solid Mechanics. first one concerns study time-dependent constitutive law with unilateral constraints memory term. second related frictional contact problem viscoelastic materials. For both problems describe physical setting, list assumptions data results.