Asymptotic behavior of a reaction-diffusion problem with delay and reaction term concentrated in the boundary

Gleiciane Da Silva Aragão, Sergio Muniz Oliva
2011 São Paulo Journal of Mathematical Sciences  
In this work we analyze the asymptotic behavior of the solutions of a reaction-diffusion problem with delay when the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter goes to zero. This analysis of the asymptotic behavior uses, as a main tool, the convergence result found in [3] . Here, we prove the existence of a family of global attractors and that this family is upper semicontinuous at = 0. We also prove the continuity
more » ... ve the continuity of the set of equilibria at = 0. → n (x) : x ∈ ∂Ω and σ ∈ [0, )},
doi:10.11606/issn.2316-9028.v5i2p347-376 fatcat:up7fxvemfrbhrh7urpjj2ucwtm