Asymptotic analysis a perturbed Robin problem in a planar domain

: We consider a perforated domain Ω( ǫ ) of R 2 with a small hole of size ǫ and we study the behavior of the solution of a mixed Neumann-Robin problem in Ω( ǫ ) as the size ǫ of the small hole tends to 0. In addition to the geometric degeneracy of the problem, the ǫ -dependent Robin condition may degenerate into a Neumann condition for ǫ = 0 and the Robin datum may diverge to infinity. Our goal is to analyze the asymptotic behavior of the solutions to the problem as ǫ tends to 0 and understand how the boundary condition affects the behavior of the solutions when ǫ is close to 0.

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