Analysis and discretization of the Ohta–Kawasaki equation with forcing and degenerate mobility

The Ohta–Kawasaki equation models the mesoscopic phase separation of immiscible polymer chains that form diblock copolymers, with applications in directed self-assembly for lithography. We perform a mathematical analysis of this model under degenerate mobility and a mass source, proving the existence of weak solutions via an approximation scheme for the mobility function. Additionally, we propose a fully discrete scheme for the non-degenerate system and demonstrate the existence and uniqueness of its discrete solution, showing that it inherits essential structural-preserving properties. Finally, we conduct numerical experiments to compare the Ohta–Kawasaki system with the classical Cahn–Hilliard model, highlighting the impact of the repulsion parameter on the phase separation dynamics.