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

Aaron Brunk () and Marvin Fritz ()
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Aaron Brunk: Johannes Gutenberg University
Marvin Fritz: Austrian Academy of Sciences

Partial Differential Equations and Applications, 2025, vol. 6, issue 6, 1-33

Abstract: 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 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.

Keywords: Ohta–Kawasaki equation; Nonlocal Cahn–Hilliard equation; Existence of weak solutions; Galerkin approximation; Fully discrete scheme; Structure-preserving method; 35A01; 35A02; 35D30; 35Q92 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00362-x

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