RT Journal Article
T1 Dynamics in dumbbell domains III. Continuity of attractors
A1 Arrieta Algarra, José María
A1 Carvalho, Alexandre N.
A1 Lozada-Cruz, Germán
AB In this paper we conclude the analysis started in [3] and continued in [4] con-cerning the behavior of the asymptotic dynamics of a dissipative reactions di_usion equation in a dumbbell domain as the channel shrinks to a line segment. In [3], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [4], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in Lp and H1 norms
PB Elsevier
SN 0022-0396
YR 2009
FD 2009
LK https://hdl.handle.net/20.500.14352/42008
UL https://hdl.handle.net/20.500.14352/42008
LA eng
NO MEC
NO Programa de Financiaci_on de Grupos de Investigaci_on UCM-Comunidad de Madrid CCG07-UCM/ESP-2393. Grupo 920894
NO SIMUMAT-Comunidad de Madrid
NO CNPq
NO CAPES/DGU
NO FAPESP
DS Docta Complutense
RD 19 abr 2025