Homogenization of boundary value problems posed on rough domains has paramount importance in real life problems. Materials with oscillating (rough) boundary are used in many industrial applications like micro strip radiator and nano technologies, biological systems, fractal-type constructions, etc. In this talk, we will be focusing on homogenization of optimal control problems. We will begin with homogenization of a boundary control problem on an oscillating pillar type domain. Then, we will consider a time-dependent control problem posed on a little more general domain called branched structure domain. Asymptotic analysis of this interior control problem will be explained. Next, we will present a generalized unfolding operator that we have developed for a general oscillatory domain. Using this unfolding operator, we study the homogenization of a non-linear elliptic problem on this general highly oscillatory domain. Also, we analyse an optimal control problem on a circular oscillating domain with the assistance of this operator. Finally, we consider a non-linear optimal control problem on the above mentioned general oscillatory domain and study the asymptotic behaviour.

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Last updated: 13 Jun 2024