Description
PDE & Numerical Analysis Seminar
Date and Time: 16th October 2018, at 4PM
Venue: Ramanujan Hall, Mathematics Department.
Speaker: Prof. Ravi Prakash, University of Concepcion, Chile.
Title: "Homogenization: Oscillating Boundary Domains"
Abstract of the seminar:
Homogenization is a branch of science where we try to understand microscopic structures via a macroscopic medium. Hence, it has applications in various branches of science and engineering. This study is basically developed from material science in the creation of composite materials though the contemporary applications are much far and wide. It is a process of understanding the microscopic behavior of an in-homogeneous medium via a homogenized medium. Mathematically, it is a kind of asymptotic
analysis. We are interested in the asymptotic behavior of elliptic boundary value problems posed in domains with highly oscillating boundary. In fact, we will consider different types of unfolding operators to study many types of oscillating boundary domains with various model problems posed in them. We will also see some interesting optimal boundary control problem posed in such domains. In total, the presentation will start from the asymptotic behavior of Laplacian in a simple rectangular oscillating boundary domains to the future possibilities of the shapes of oscillations in the boundary keeping in mind the mathematical issues arise in topology optimization.