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arXiv:1601.06271 [math.AP]AbstractReferencesReviewsResources

Minimisers of the Allen-Cahn equation on hyperbolic graphs

Blaz Mramor

Published 2016-01-23Version 1

We investigate minimal solutions of the Allen-Cahn equation on a Gromov-hyperbolic graph. Under some natural conditions on the graph, we show the existence of non-constant uniformly-bounded minimal solutions with prescribed asymptotic behaviours. For a phase field model on a hyperbolic graph, such solutions describe energy-minimising steady-state phase transitions that converge towards prescribed phases given by the asymptotic directions on the graph.

Comments: arXiv admin note: text overlap with arXiv:1508.06751
Categories: math.AP
Subjects: 58J05, 35J20, 53C23
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