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# Optimal Control Problems in a Domain with Oscillating Boundary and Homogenization

Bidhan Chandra Sardar, Department of Mathematics, Indian Institute of Science, Bangalore
 Speaker Bidhan Chandra Sardar, Department of Mathematics, Indian Institute of Science, Bangalore Aug 08, 2016 from 04:00 PM to 05:00 PM LH 006 vCal iCal

Abstract: We consider a two dimensional oscillating domain (comb shape type) $\Omega_{\epsilon}$ consists of a fixed bottom region $\Omega^-$ and an oscillatory (rugose) upper region $\Omega_{\epsilon}^{+}$. We introduce an optimal control problems in $\Omega_{\epsilon}$ for the Laplacian operator. There are mainly two types of optimal control problems; namely distributed control and boundary control. In this talk, first we consider distributed optimal control problem, where the control is supported on the oscillating part $\Omega_{\epsilon}^{+}$ with periodic controls and with Neumann condition on the oscillating boundary $\gamma_{\epsilon}$. Secondly, we introduce boundary optimal control problem, control applied through Neumann boundary condition on the oscillating boundary $\gamma_{\epsilon}$ with suitable scaling parameters. Our main aim is to characterize the controls and study the limiting analysis (as $\epsilon \to 0$) of the optimal solution.

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