Existence of continuous solutions to evolutionary quasi-variational inequalities with applications

Abstract

The author presents dynamic elastic traffic equilibrium problems with data depending explicitly on time and studies under which assumptions the continuity of solutions with respect to the time can be ensured. In particular, regularity results for solutions to time-dependent quasi-variational inequalities associated to a general class of closed lower semicontinuous multifunctions will be showed. These results will be obtained making use of the property of the Mosco’s convergence. At last, it will be applied an example of the dynamic elastic traffic equilibrium problem.