RT Journal Article
T1 Dynamics in dumbbell domains. II: The limiting problem
A1 Arrieta Algarra, José María
A1 Carvalho, Alexandre N.
A1 Lozada-Cruz, Germán
AB In this work we continue the analysis of the asymptotic dynamics of reaction–diffusion problems in a dumbbell domain started in [J.M. Arrieta, A.N. Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2) (2006) 551–597]. Here we study the limiting problem, that is, an evolution problem in a “domain” which consists of an open, bounded and smooth set Ω⊂RN with a curve R0 attached to it. The evolution in both parts of the domain is governed by a parabolic equation. In Ω the evolution is independent of the evolution in R0 whereas in R0 the evolution depends on the evolution in Ω through the continuity condition of the solution at the junction points. We analyze in detail the linear elliptic and parabolic problem, the generation of linear and nonlinear semigroups, the existence and structure of attractors.
PB Elsevier
SN 0022-0396
YR 2009
FD 2009
LK https://hdl.handle.net/20.500.14352/42007
UL https://hdl.handle.net/20.500.14352/42007
LA eng
NO MEC
NO SIMUMAT-Comunidad de Madrid
NO CNPq
NO CAPES/DGU
NO FAPESP
DS Docta Complutense
RD 8 jun 2025