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INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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An Autonomous Institution, Ministry of Human Resource Development, Govt. of India
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Seminars and Colloquia

Mathematics

Optimal Control in Stochastic Landau-Lipschitz-Gilbert Equation 
 
Thu, Sep 20, 2018,   04:00 PM to 05:00 PM at Madhava Hall

Dr. Ananta Kumar Majee
IIT Delhi

In this presentation, we study an optimal control problem for the stochastic Landau- Lipschitz-Gilbert equation on a bounded domain inR(= 1,2,3). We first establish existence of a relaxed optimal control for relaxed version of the problem. As the control acts linearly in the equation, we then establish existence of an optimal control for the underlying problem. Moreover, convergence of a structure preserving finite element approximation for = 1 and physically relevant computational studies will be discussed.

Furthermore, we study an optimal control problem of interacting ferromagnetic particles which are immersed into a heat bath through the application of a distributed exterior field minimizing a quadratic cost functional. With the dynamic programming principle, we show the existence of a unique strong solution of the optimal control problem. With a Hopf-Cole transformation the related nonlinear Hamilton-Jacobi-Bellman equation is re-cast into a linear PDE on the manifold = (S2), whose classical solution is represented with a Feynman-Kac formula. We propose to use this probabilistic representation to numerically study optimal switching dynamics with Monte- Carlo simulations

 

 

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