Time: 9h30, Tuesday, June 30, 2015

Location: Room 4, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract: Data assimilation is the problem of determining the initial condition of  evolutional systems from some observations in the past and present. This is one of the most important issues in forecasting. Data assimilation is difficult, since it is nonlinear, highly ill-posed and extremely large dimensional. In this thesis we focus on data assimilation of a heat transfer system with time dependent conductivity from 1) present observations, 2) interior (integral) observations, 3) boundary observation. We propose variational methods for solving them, and discretize them by finite difference splitting methods which reduce high dimensional problems to a sequence of one-dimensional ones. Numerical examples are tested showing our methods are efficient.