Date/heure
16 octobre 2020
11:00 - 12:00
Oratrice ou orateur
Maria Neuss-Radu
Catégorie d'évènement Séminaire EDP, Analyse et Applications (Metz)
Résumé
We consider a nonlinear reaction–diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order $epsilon$, and the equation inside the layer depends on the parameter $epsilon$. We consider the critical scaling of the diffusion coefficients in the channels and nonlinear Neumann-boundary condition on the channels’ lateral boundaries. We derive effective models in the limit $epsilon to 0 $, when the channel-domain is replaced by an interface $Sigma$ between the two bulk-domains. Due to the critical size of the diffusion coefficients, we obtain jumps for the solution and its normal fluxes across $Sigma$, involving the solutions of local cell problems on the reference channel in every point of the interface $Sigma$. This is a joint work with Markus Gahn (University of Heidelberg)