Dynamics in dumbbell domains I. Continuity of the set of equilibria - Arrieta, Jose M.; Carvalho, Alexandre N.; Lozada-Cruz, German (Elsevier B.V., 2006)
We 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. (c) 2006 Elsevier B.V. All rights reserved.
Keywords: reaction-diffusion equation; stationary solutions; dumbbell domains; continuity