Evolutionary variational inequalities

Abstract

The variational inequalities studied in this work are evolutionary since they in- volve the time derivative of the solution. In this research we reached to the main purpose and conclude that this kind of inequalities has a unique solution and this may be proved by using several methods similar to penalty, elliptic regularization methods we showed during the develop- ment of this thesis. Despite this analysis, the subject of variational inequalities remains open to wide research and perspective such as: ✍ Evolutionary variational inequalities of the second kind. ✍ Hyperbolic variational inequalities. ✍ Quasi variational inequalities.