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Title: Segregation and domain formation in non-local multi-species aggregation equations
A system of aggregation equations describing nonlocal interaction of two species is studied. When interspecies repulsive forces dominate intra-species repulsion, phase segregation may occur. This leads to the formation of distinct phase domains, separated by moving interfaces. The one dimensional interface problem is formulated variationally, and conditions for existence and nonexistence are established. The singular limit of large and short-ranged repulsion in two dimensions is then considered, leading to a two-phase free boundary problem describing the evolution of phase interfaces. Long term dynamics are investigated computationally, demonstrating coarsening phenomenon quantitatively different from classical models of phase separation. Finally, the interplay between long-range interspecies attraction and interfacial energy is illustrated, leading to pattern formation.  more » « less
Award ID(s):
1908968
PAR ID:
10529202
Author(s) / Creator(s):
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Physica D: Nonlinear Phenomena
Volume:
456
Issue:
C
ISSN:
0167-2789
Page Range / eLocation ID:
133936
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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