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Dynamics in dumbbell domains I. Continuity of the set of equilibria |
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| Authors: | José M Arrieta Alexandre N Carvalho German Lozada-Cruz |
| Institution: | a Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain b Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil c Departamento de Matemática, IBILCE, UNESP, 15054-000 São José do Rio Preto SP, Brazil |
| Abstract: | 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. |
| Keywords: | primary 35B40 secondary 35K55 35B25 |
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