Discrete gevrey regularity attractors and uppers–semicontinuity for a finite difference approximation to the ginzburg–landau equation |
| |
| Authors: | Gabriel J Lord Andrew M Stuart |
| |
| Institution: | 1. School of Mathematical Sciences , University of Bath , Bath, Avon, BA2 7AY, U.K.;2. SCCM Program, Division of Applied Mechanics , Stanford University , Durand 252, Standford, California, 94305-4040, U.S.A |
| |
| Abstract: | A semi-discrete spatial finite difference approximation to the complex Ginzburg-Landau equation with cubic non-linearity is considered. Using the fractional powers of a sectorial operator, discrete versions of the Sobolev spaces H 5, and Gevrey classes of regularityG, are introduced.Discrete versions of some standard Sobolev space norm inequalities are proved. |
| |
| Keywords: | |
|
|
