The homogenization of the heat equation with mixed conditions on randomly subsets of the boundary
Carmen Calvo‐Jurado, Juan Casado‐Díaz, Manuel Luna‐Laynez · Conference Publications · 2013
We consider a domain in $\mathbb{R}^N$, $N\geq 3$, such that a portion of its boundary is plane.In this portion we fix a sequence $K_\epsilon$ of small subsets randomly distributed in such way that the distance between them is of order $\epsilon$ and their diameters are of order $\epsilon^\frac{N-1}{N-2}$. We study the asymptotic behavior of the heat equation with Dirichlet conditions on $K_\epsilon$ and Neumann conditions on the rest of the boundary.We prove the convergence to a limit problem with a Fourier-Robin boundary condition which has the physicalinterest of being deterministic.