Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1709567 | Applied Mathematics Letters | 2008 | 6 Pages |
Abstract
We study a class of nonlinear evolutionary equations generated by a pseudo-differential operator with the elliptic principal symbol and with nonlinearities of the form G(ux)G(ux) where cη2≤G(η)≤Cη2cη2≤G(η)≤Cη2 for large |η||η|. We demonstrate existence of a universal absorbing set, and a compact attractor, and show that the attractor is of a finite Hausdorff dimension. The stabilization mechanism is similar to the nonlinear saturation well known for the Kuramoto–Sivashinsky equation.
Related Topics
Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Michael Frankel, Victor Roytburd,