Arrieta Algarra, José MaríaCarvalho, Alexandre N.Lozada-Cruz, Germán2023-06-202023-06-2020060022-039610.1016/j.jde.2006.06.002https://hdl.handle.net/20.500.14352/49744We analyze the dynamics of a reaction–diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds.engDynamics in Dumbbell domains. I: Continuity of the set of equilibria.journal articlehttp://www.sciencedirect.com/science/journal/00220396open access517.9Reaction-diffusion equationStationary solutionsDumbbell domainscontinuityHomogeneous Neumann boundary conditionsEcuaciones diferenciales1202.07 Ecuaciones en Diferencias