Data assimilation problems and stabilization with respect to unstable manifolds

Abstract

A newmethod solving the initial data assimilation problemis proposed in the paper. Themethod is based on the results of the theory of global attractors. The numerical algorithmis formulated, its convergence is justified, analysis of computational formulas is performed. It is shown that themethod is equivalent in some sense to the construction of nontrivial trajectories of a global attractor and also to solving the stabilization problem in terms of projections onto an unstable manifold. This result allows us to consolidate the theory of iterative methods for stabilization to unstable trajectories of the hyperbolic type based on the properties of local invariant stable and unstable manifolds.