The ground-breaking nature of the project relies on the possibility of opening new horizonswith a novel mathematical formulation of physical problems.The project aim is indeed to obtain relevant mathematical results in order toget further insight into new models for phase transitions and thecorresponding evolution PDE systems. The new approach presented here turnsout to be particularly helpful within the investigation of issues like as existence, uniqueness,control, and long-time behavior of the solutions for such evolutionary PDEs.Moreover, the importance of the opportunity to apply such new theory to phase transitions liesin the fact that such phenomena arise in a variety of applied problems like, e.g.,melting and freezing in solid-liquid mixtures, phase changes in solids, crystal growth, soil freezing,damage in elastic materials, plasticity, food conservation, collisions, and so on. Fromthe practical viewpoint, the possibility to describe these phenomena in a quantitative wayhas deeply influenced the technologicaldevelopment of our society, stimulating the related mathematical interest.