Homogenization of Highly Oscillating Boundaries with Strongly Contrasting Diffusivity
Antonio Gaudiello, Ali Sili · SIAM Journal on Mathematical Analysis · 2015
We consider a linear diffusion problem, with strongly contrasting diffusivity, in a medium having a highly oscillating boundary. The problem is characterized by two small positive parameters: a parameter $\varepsilon$ describing the periodicity of the oscillating boundary and a parameter $\alpha_\varepsilon$ describing the contrasting diffusivity. As $\varepsilon$ and $\alpha_\varepsilon$ vanish, we pinpoint three different limit regimes depending on ratio $l=\lim\frac{\alpha_\varepsilon}{\varepsilon}$, according to l=0, $0