Title: Homogenization of PDEs on oscillating boundary domains with L1 data and Optimal control problems
Speaker: Renjith T. (IISc Mathematics)
Date: 27 April 2023
Time: 11 am
Venue: LH-3, Mathematics Department
This talk will comprehensively examine the homogenization of partial differential equations (PDEs) and optimal
control problems with oscillating coefficients in oscillating domains. We will focus on two specific problems.
The first is the homogenization of a second-order elliptic PDE with strong contrasting diffusivity and L1 data
in a circular oscillating domain. As the source term we are considering is in L1, we will examine the renormalized
solutions. The second problem we will investigate is an optimal control problem governed by a second-order
semi-linear PDE in an $n$-dimensional domain with a highly oscillating boundary, where the oscillations occur in
$m$ directions, with $1< m < n$. We will explore the asymptotic behavior of this problem by homogenizing the
corresponding optimality systems.