# American Institute of Mathematical Sciences

February  2017, 37(2): 983-1012. doi: 10.3934/dcds.2017041

## A stationary core-shell assembly in a ternary inhibitory system

 Department of Mathematics, The George Washington University, Washington, DC 20052, USA

* Corresponding author: Xiaofeng Ren

Received  March 2015 Revised  January 2016 Published  November 2016

A ternary inhibitory system motivated by the triblock copolymer theoryis studied as a nonlocal geometric variational problem. The free energyof the system is the sum of two terms: the total size of the interfacesseparating the three constituents, and a longer ranging interaction energythat inhibits micro-domains from unlimited growth. In a particular parameterrange there is an assembly of many core-shells that exists as a stationaryset of the free energy functional. The cores form regions occupied by thefirst constituent of the ternary system, the shells form regionsoccupied by the second constituent, and the background is taken by thethird constituent. The constructive proof of the existence theorem revealsmuch information about the core-shell stationary assembly: asymptoticallyone can determine the sizes and locations of all the core-shells in theassembly. The proof also implies a kind of stability for the stationaryassembly.

Citation: Xiaofeng Ren, Chong Wang. A stationary core-shell assembly in a ternary inhibitory system. Discrete & Continuous Dynamical Systems - A, 2017, 37 (2) : 983-1012. doi: 10.3934/dcds.2017041
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##### References:
A double bubble assembly on the left and a core-shell assembly on the right
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