The complex Ginzburg - Landau equation on large and unbounded domains: sharper bounds and attractors
- 1 January 1997
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 10 (1) , 199-222
- https://doi.org/10.1088/0951-7715/10/1/014
Abstract
Using weighted Lp--norms we derive new bounds on the long--time behavior ofthe solutions improving on the known results of the polynomial growth with respectto the instability parameter. These estimates are valid for quite arbitrary, possiblyunbounded domains. We establish precise estimates on the maximal influence ofthe boundaries on the dynamics in the interior. For instance, the attractor A ` forthe domain (\Gamma`; `)dwith periodic boundary conditions is upper semicontinuous...Keywords
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