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

Abstract

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 an external force, proving the existence of weak solutions via an approximation scheme for the mobility function. Additionally, we propose a fully discrete scheme for the 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.

References in corpus (4)

• Time-fractional Cahn-Hilliard equation: Well-posedness, degeneracy, and numerical solutions
• Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy
• A globally convergent modified Newton method for the direct minimization of the Ohta-Kawasaki energy with application to the directed self-assembly of diblock copolymers
• On a Cahn-Hilliard equation for the growth and division of chemically active droplets modeling protocells