Validation of the bifurcation diagram in the 2D Ohta-Kawasaki problem

We develop a rigorous numerical method to compare local minimizers of the Ohta-Kawasaki functional in two dimensions. In particular, we validate the phase diagram identifying regions of parameter space where rolls are favorable, where hexagonally packed spots have lowest energy and finally where the...

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Bibliographic Details
Published inNonlinearity Vol. 30; no. 4; pp. 1584 - 1638
Main Authors van den Berg, Jan Bouwe, Williams, J F
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.04.2017
Subjects
bifurcation diagram
domain optimization
Ohta-Kawasaki
rigorous numerics
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Summary:We develop a rigorous numerical method to compare local minimizers of the Ohta-Kawasaki functional in two dimensions. In particular, we validate the phase diagram identifying regions of parameter space where rolls are favorable, where hexagonally packed spots have lowest energy and finally where the constant mixed state does. More generally, we present a method to rigorously determine such features in problems where optimal domain sizes are not known a priori.
Bibliography:NON-101434.R1
London Mathematical Society
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aa60e8