Well-posedness and asymptotic behavior of an aggregation model with intrinsic interactions on sphere and other manifolds
Keyword(s):
The Mean
◽
We investigate a model for collective behavior with intrinsic interactions on Riemannian manifolds. We establish the well-posedness of measure-valued solutions (defined via mass transport) on sphere, as well as investigate the mean-field particle approximation. We study the long-time behavior of solutions to the model on sphere, where the primary goal is to establish sufficient conditions for a consensus state to form asymptotically. Well-posedness of solutions and the formation of consensus are also investigated for other manifolds (e.g., a hypercylinder).
2007 ◽
Vol 5
(5)
◽
pp. 11-19
◽
Keyword(s):
2014 ◽
Vol 24
(14)
◽
pp. 2743-2783
◽
Keyword(s):
2020 ◽
Vol 130
(4)
◽
pp. 1879-1896
2009 ◽
Vol 69
(6)
◽
pp. 1644-1661
◽
Keyword(s):
2007 ◽
Vol 18
(1)
◽
pp. 15-38
◽
Keyword(s):