Well-posedness of a second-order time and state-dependent degenerate sweeping process

We investigate a new class of second-order time and state-dependent degenerate sweeping processes in a separable Hilbert space. We prove existence and uniqueness of the solution using an implicit time discretization scheme. Under a hypomonotonicity assumption on the normal cone, we ensure the strong convergence of the approximating sequences. We complete our study with a continuous dependence result of the solution with respect to the initial data. Our framework unifies and extends some known models and is applied to a second-order variational inequality.