Preprint of the project: DFG research group "Spectral analysis, asymptotic distributions and stochastic dynamics"

Numerical approximation and spectral analysis of infinite-dimensional dynamical systems

04-013 Wolf-Jürgen Beyn, Vasiliy S. Kolezhuk, Sergei Pilyugin.
Convergence of discretized attractors for parabolic equations on the line


We show that, for a semilinear parabolic equation on the real line satisfying a dissipativity condition, global attractors of time-space discretizations converge (with respect to the Hausdorff semi-distance) to the attractor of the continuous system as the discretization steps tend to zero. The attractors considered correspond to pairs of function spaces (in the sense of Babin-Vishik) with weighted and locally uniform norms (taken from Mielke-Schneider) used for both the continuous and the discrete system.