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On a Quaternary Non-Local Isoperimetric Problem
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On a Quaternary Non-Local Isoperimetric Problem

Abstract

We study a two-dimensional quaternary inhibitory system. This free energy functional combines an interface energy favoring micro-domain growth with a Coulomb-type long range interaction energy which prevents micro-domains from unlimited spreading. Here we consider a limit in which three species are vanishingly small, but interactions are correspondingly large to maintain a nontrivial limit. In this limit two energy levels are distinguished: the highest order limit encodes information on the geometry of local structures as a three-component isoperimetric problem, while the second level describes the spatial distribution of components in global minimizers. Geometrical descriptions of limit configurations are derived.

Authors

Alama S; Bronsard L; Lu X; Wang C

Publication date

July 23, 2023

DOI

10.48550/arxiv.2307.12504

Preprint server

arXiv
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