About the Structure of Attractors for a Nonlocal Chafee-Infante Problem
Keyword(s):
In this paper, we study the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee the uniqueness of the Cauchy problem. First, we analyse the existence and properties of stationary points, showing that the problem undergoes the same cascade of bifurcations as in the Chafee-Infante equation. Second, we study the stability of the fixed points and establish that the semiflow is a dynamic gradient. We prove that the attractor consists of the stationary points and their heteroclinic connections and analyse some of the possible connections.
2006 ◽
Vol 324
(1)
◽
pp. 381-396
◽
Keyword(s):
2016 ◽
Vol 8
(2)
◽
pp. 168781401662989
◽
2007 ◽
Vol 240
(2)
◽
pp. 279-323
◽
2012 ◽
Vol 67
(6-7)
◽
pp. 355-362
◽
2013 ◽
Vol 26
(3)
◽
pp. 315-317
◽
2016 ◽
Vol 444
(2)
◽
pp. 1479-1489
◽
Keyword(s):
Keyword(s):
2001 ◽
Vol 256
(2)
◽
pp. 513-524
Keyword(s):
Keyword(s):