Numerische Approximation und Spektrale Analysis unendlich-dimensionaler Dynamischer Systeme
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.
