Evolution variational inequalities and projected dynamical systems with application to human migration

In this paper, we explore the relationship between projected dynamical systems and evolution variational inequalities (also sometimes referred to as parabolic variational inequalities). The methodology of evolution variational inequalities is then utilized for the first time to model the dynamic adjustment of a socio-economic process in the context of human migration. The questions of dynamics and convergence of algorithms in this framework are addressed and answered. In particular, we provide existence and uniqueness results for the solution path without assuming Lipschitz continuity and propose a finite-difference scheme for the solution of the human migration problem. The algorithm, an ordinary implicit scheme, is a discrete-time version of the model. Its convergence estimate is also established.