ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

1991 MS Classification: 65, 35, 58 Pilyugin, Sergei Yu., St. -Petersburg University, Russia Shadowing and perturbation of attractors in discretized parabolic equations Let S(t) be the semigroup in H_{0}^{1}(0, 1) generated by a parabolic equation

u_{t} = u_{xx} + f(u), u ∈ R, x ∈ [0, 1],

with the Dirichlet boundary conditions. Assume that all fixed points of S(t) are hyperbolic. It is shown that in this case approximate trajectories given by a semiimplicit discretization with space step d and time step h are shadowed by exact trajectories on unbounded time intervals with accuracy L(d + h), where L is an absolute constant. Hausdorff distances between “exact“ and “discretized” global attractors are estimated. Part of these results is joint work with S. Larsson.