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Global minimisers for anisotropic attractive–repulsive interactions

Part of: Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  22 October 2019

GUNNAR KAIB ,
KYUNGKEUN KANG  and
ANGELA STEVENS
GUNNAR KAIB
Affiliation:
Ellerstraße 69, 40227 Düsseldorf, Germany, email: gunnar.kaib@web.de
KYUNGKEUN KANG
Affiliation:
Department of Mathematics, Yonsei University, Seoul, Republic of Korea, email: kkang@yonsei.ac.kr
ANGELA STEVENS
Affiliation:
Applied Mathematics, University of Münster, Einsteinstr. 62, D-48149 Münster, Germany, email: angela.stevens@wwu.de
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Abstract

We prove the existence of global minimisers for a class of attractive–repulsive interaction potentials that are in general not radially symmetric. The global minimisers have compact support. For potentials including degenerate power-law diffusion, the interaction potential can be unbounded from below. Further, a formal calculation indicates that for non-symmetric potentials global minimisers may neither be radial symmetric nor unique.

Keywords

Anisotropic attractive–repulsive interactionglobal minimisers

MSC classification

Primary: 35A15: Variational methods
Secondary: 35K65: Degenerate parabolic equations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 5 , October 2020 , pp. 854 - 870
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Copyright
© Cambridge University Press 2019

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