Estimation of a temporally and spatially varying diffusion coefficient in a parabolic system by an augmented Lagrangian technique (Q1179037)

A temporally and spatially varying coefficient is to be estimated in a one-dimensional parabolic problem which has applications in biological modelling and fluid flow in porous media. A hybrid method combining the advantages of the equation error approach and of the output least squares method is proposed. An augmented Lagrangian iterative algorithm is introduced and its convergence demonstrated. The essential technical tool for the convergence proof is a coercivity condition. It is shown that this condition also guarantees the stability of the solutions with respect to perturbations in the observation. Special cases in which the coercivity condition holds are analyzed. A numerical example is given.