Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
荆文甲 博士, 清华大学
Inviter:
徐丽 博士
Title:
On the homogenization of Dirichlet problems in perforated domain
Time & Venue:
2018.9.28 15:00-16:00 Z311
Abstract:
We consider the homogenization of Dirichlet problems for the Laplace operator in perforated domains, and present a unified approach adaptive to the ratio between the sizes of the perforating holes and the typical cells. For finite hole-cell size ratios, we adopt the standard oscillating test function method; for vanishing hole-cell size ratios, we add in the asymptotic behaviors of a properly rescaled cell problem. When the hole-cell size ratio is critically small, our method recovers "the strange term from nowhere" due to Cioranescu and Tartar; the method also reveals how this critical case intrinsically relates to the case of relatively largers holes, where the limiting equation becomes algebraic, and to the case of smaller holes, where the limiting equation ignores the holes. I will comment on quantitative estimates and on the random settings.