On the Convergence of the Ohta–Kawasaki Equation to Motion by Nonlocal Mullins–Sekerka Law

DOI10.1137/090768643zbMath1230.49008arXiv0912.0219OpenAlexW2962700795MaRDI QIDQ2999868

Nam Q. Le

Publication date: 17 May 2011

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0219

zbMATH Keywords

De Giorgi conjectureOhta-Kawasaki equationGamma-convergence of gradient flowsmicrophase separation in diblock copolymersnonlocal Mullins-Sekerka lawtransport estimate

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Singular perturbations in context of PDEs (35B25) Methods involving semicontinuity and convergence; relaxation (49J45) Initial value problems for higher-order parabolic equations (35K30) Variational principles of physics (49S05) PDEs in connection with control and optimization (35Q93)

Related Items (9)

Gamma-convergence of generalized gradient flows with conjugate type ⋮ Global existence and stability for the modified Mullins-Sekerka and surface diffusion flow ⋮ The systems of nonlinear gradient flows on metric spaces and their \(\Gamma\)-convergence ⋮ The mean curvature at the first singular time of the mean curvature flow ⋮ The Cahn–Hilliard–Oono equation with singular potential ⋮ Weak solutions of Mullins-Sekerka flow as a Hilbert space gradient flow ⋮ Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers ⋮ An MBO scheme for minimizing the graph Ohta-Kawasaki functional ⋮ On the second inner variations of Allen-Cahn type energies and applications to local minimizers

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