Periodicity and uniqueness of global minimizers of an energy functional containing a long-range interaction

Xinfu Chen, Yoshihito Oshita

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

We consider, on an interval of arbitrary length, global minimizers of a class of energy functional containing a small parameter e and a long-range interaction. Such functionals arise from models for phase separation in diblock copolymers and from stationary solutions of FitzHugh-Nagumo systems. We show that every global minimizer is periodic with a period of order ε 1/3. Also, we identify the number of global minimizers and provide asymptotic expansions for the periods and global minimizers.

Original languageEnglish
Pages (from-to)1299-1332
Number of pages34
JournalSIAM Journal on Mathematical Analysis
Volume37
Issue number4
DOIs
Publication statusPublished - 2005
Externally publishedYes

Fingerprint

Global Minimizer
Long-range Interactions
Energy Functional
Phase separation
Periodicity
Block copolymers
Uniqueness
FitzHugh-Nagumo
Copolymer
Phase Separation
Stationary Solutions
Small Parameter
Asymptotic Expansion
Interval
Arbitrary

Keywords

  • Elliptic systems
  • Singular perturbation
  • Transition layer

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Applied Mathematics
  • Numerical Analysis

Cite this

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