TY - JOUR
T1 - Validation of the bifurcation diagram in the 2D Ohta-Kawasaki problem
AU - van den Berg, Jan Bouwe
AU - Williams, J.F.
PY - 2017/4
Y1 - 2017/4
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85016152021&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85016152021&partnerID=8YFLogxK
U2 - 10.1088/1361-6544/aa60e8
DO - 10.1088/1361-6544/aa60e8
M3 - Article
SN - 0951-7715
VL - 30
SP - 1584
EP - 1638
JO - Nonlinearity
JF - Nonlinearity
IS - 4
ER -
