Asymptotic behavior of diffusion problems in a domain made of two cylinders of different diameters and lengths
Juan Casado‐Díaz, Manuel Luna‐Laynez, François Murat · Comptes Rendus Mathématique · 2003
We study the asymptotic behavior of the solution of a diffusion problem posed in the union of a cylinder of small diameter and fixed length with another cylinder with much smaller diameter and length. The Dirichlet condition is assumed to hold at both extremities of this domain. Depending on the relative size of the parameters, we show that the boundary condition of the one-dimensional limit problem is a Dirichlet, Fourier or Neumann condition. We also prove a corrector result for every case.