TY - JOUR

T1 - Convergence of discretized attractors for parabolic equations on the line

AU - Beyn, W. J.

AU - Kolezhuk, V. S.

AU - Pilyugin, S. Yu

N1 - Funding Information: Aknowledgments. W.-J. Beyn and S. Yu. Pilyugin were supported by DFG Research Group “Spectral analysis, asymptotic distributions, and stochastic dynamics.” V. S. Kolezhuk and S. Yu. Pilyugin were supported by the Russian Foundation for Basic Research (project 02-01-00675) and by the Ministry of Education of Russia (project E02-1.0-65). V. S. Kolezhuk was supported by the Schlumberger program of PhD grants.

PY - 2006/7

Y1 - 2006/7

N2 - 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 both for the continuous and discrete systems. Bibliography: 13 titles.

AB - 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 both for the continuous and discrete systems. Bibliography: 13 titles.

UR - http://www.scopus.com/inward/record.url?scp=33744820350&partnerID=8YFLogxK

U2 - 10.1007/s10958-006-0190-y

DO - 10.1007/s10958-006-0190-y

M3 - Article

AN - SCOPUS:33744820350

VL - 136

SP - 3655

EP - 3671

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 2

ER -