Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers

The Ohta-Kawasaki model for diblock-copolymers is well known to the scientific community of diffuse-interface methods. To accurately capture long-time evolution moving interfaces, we present a derivation corresponding sharp-interface limit using matched asymptotic expansions, and show that limiting process leads Hele-Shaw type interface problem. numerical treatment more complicated due stiffness equations. address this problem, boundary integral formulation sharp model. Starting with governing equations defined on separate phase domains, develop valid multi-connected domains in 2D plane. For simplicity assume our problem driven by uniform Dirichlet condition circular far-field boundary. involves both double- single-layer potentials modified condition. In particular, allows one compute nonlinear dynamics non-equilibrium system pattern formation an equilibrating system. Numerical tests evolving slightly perturbed (separating two phases) are excellent agreement linear analysis, demonstrating method stable, efficient spectrally accurate space.