Approximation of attractors for evolution equations with the help of attractors for finite systems
The problem of approximation of attractors for semidynamical systems (SDS) in a metric space is considered. Let some (exact) SDS possessing an attractor M be inaccurately defined, i.e., another SDS, which is close in some sense to the exact one, be given. The problem is to find a set M that is close to M in the Hausdorff metric. A finite procedure for construction of M is suggested. The results obtained are suitable for numerical construction of attractors for a rather large class of systems, including the ones generated by the Lorenz equations. Bibliography: 8 titles.
KeywordsEvolution Equation Large Class Finite System Lorenz Equation Numerical Construction
Unable to display preview. Download preview PDF.
- 2.O. A. Ladyzhenskaya, “Globally stable difference schemes and their attractors”, (Preprint LOMI) R-5-91, Leningrad (1991).Google Scholar
- 3.A. V. Babin and M. I. Vishik, Attractors of Evolution Equations [in Russian], Nauka, Moscow (1989).Google Scholar
- 8.K. Kuratowski, Topology, Academic Press, New York (1968).Google Scholar