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Mathematics > Numerical Analysis

arXiv:2411.09498 (math)
[Submitted on 14 Nov 2024]

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

Authors:Aaron Brunk, Marvin Fritz
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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.
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP)
Cite as: arXiv:2411.09498 [math.NA]
  (or arXiv:2411.09498v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2411.09498

Submission history

From: Marvin Fritz [view email]
[v1] Thu, 14 Nov 2024 15:06:20 UTC (18,212 KB)
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