Periodic homogenization of a diffusion equation
= Periodic homogenization of a diffusion equation
For $u_t=\partial_x[a(x/\epsilon)u_x]$ with positive periodic $a$, the one-dimensional homogenized diffusivity is the harmonic mean $a_{\rm eff}=\langle a^{-1}\rangle^{-1}$. Microscopic flux continuity produces this harmonic rather than arithmetic averaging.