Projected Dynamical Systems and Evolutionary 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.