On the cahn-hilliard-oono equation with singular potential and volume constraint

We consider a new version of the Cahn-Hilliard-Oono equation with logarithmic potential of Flory-Huggins type, where we include a nonlocal constraint term acting on the spatial mean of the order parameter phi in order to force it remain inside the physical interval [-1, 1] even in presence of an external mass source. By applying a modification of the methods that have been used to study the standard Cahn-Hilliard equation, it is then possible to discuss the existence and uniqueness of weak solutions and the regularity of solutions under appropriate assumptions. Applications of our results to tumor growth models are also detailed.