%APromislow, Keith%AWu, Qiliang%BJournal Name: Discrete and Continuous Dynamical Systems - S; Journal Volume: 15; Journal Issue: 9
%D2022%I
%JJournal Name: Discrete and Continuous Dynamical Systems - S; Journal Volume: 15; Journal Issue: 9
%K
%MOSTI ID: 10382648
%PMedium: X
%TUndulated bilayer interfaces in the planar functionalized Cahn-Hilliard equation
%XExperiments with diblock co-polymer melts display undulated bilayers that emanate from defects such as triple junctions and endcaps, [8]. Undulated bilayers are characterized by oscillatory perturbations of the bilayer width, which decay on a spatial length scale that is long compared to the bilayer width. We mimic defects within the functionalized Cahn-Hillard free energy by introducing spatially localized inhomogeneities within its parameters. For length parameter \begin{document}$ \varepsilon\ll1 $\end{document}, we show that this induces undulated bilayer solutions whose width perturbations decay on an \begin{document}$ O\!\left( \varepsilon^{-1/2}\right) $\end{document} inner length scale that is long in comparison to the \begin{document}$ O(1) $\end{document} scale that characterizes the bilayer width.

%0Journal Article