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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月17日

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  • Aaron Brunk,
  • Marvin Fritz

摘要

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.