Speaker : Minha Yoo (National Institute for Mathematical Science)
Title : Homogenization of elliptic and parabolic soft inclusions
Time : 2017-02-14 (Tue) 10:30 - 11:30
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: In this talk, we consider periodic Soft inclusion problems of elliptic and parabolic linear equation of non-divergence form. Usually, it is called Soft inclusion problems to find effective conductivity of composites consisting of a medium with non-conducting grains. Mathematically, non-conducting grains are described by union of disjoint holes with periodicity epsilon. For each epsilon, the unique current density function (the solution of epsilon problem) u-epsilon exists for a given boundary data. We note that, at the boundary of grains, the Neumann data of u-epsilon vanishes. Our main interest is to show the uniform convergence of u-epsilon and to find "effective equation" what the limit of u-epsilon satisfy.