Edgar Allen identified and outlined the role of female sex hormones [2] and discovered estrogen [3] in the early 1900s in the US. In 1923, Allen, through his research with mice, isolated the primary ovarian hormone [4], later renamed estrogen [3], from ovarian follicles and tested its effect through injections in the uterine tissues of mice. Allen's work on estrogen [3], enabled researchers to ...

This thesis aims to introduce and analyse a primal-dual active set strategy for solving Allen-Cahn variational inequalities. We consider the standard Allen-Cahn equation with non-local constraints and a vector-valued Allen-Cahn equation with and without non-local constraints. Existence and uniqueness results are derived in a formulation involving Lagrange multipliers for local and non-local con...