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

Xinfu Chen; Yoshihito Oshita

doi:10.1137/S0036141004441155

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

Xinfu Chen, Yoshihito Oshita

Research output: Contribution to journal › Article › peer-review

41 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 language	English
Pages (from-to)	1299-1332
Number of pages	34
Journal	SIAM Journal on Mathematical Analysis
Volume	37
Issue number	4
DOIs	https://doi.org/10.1137/S0036141004441155
Publication status	Published - Dec 1 2005
Externally published	Yes

Keywords

Elliptic systems
Singular perturbation
Transition layer

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/S0036141004441155

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AB - 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.

KW - Elliptic systems

KW - Singular perturbation

KW - Transition layer

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

Abstract

Keywords

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