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global minimisers

European Journal of Applied Mathematics (1)

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1 results

Global minimisers for anisotropic attractive–repulsive interactions
Part of
- Parabolic equations and systems
- Partial differential equations
GUNNAR KAIB, KYUNGKEUN KANG, ANGELA STEVENS
Journal:

European Journal of Applied Mathematics / Volume 31 / Issue 5 / October 2020

Published online by Cambridge University Press:

22 October 2019, pp. 854-870
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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.