Projected Dynamical Systems and Evolutionary (time-dependent) Variational Inequalities via Hilbert Spaces with Applications

In this paper we make explicit the connection between projected dynamical systems on Hilbert spaces and evolutionary variational inequalities. We give a novel formulation that unifies the underlying constraint sets for such inequalities, which arise in time-dependent traffic network, spatial price, and a variety of financial equilibrium problems. We emphasize the importance of the results in applications and provide a traffic network numerical example in which we compute the curve of equilibria.