10.1016/j.aml.2007.03.023

Stability for a class of nonlinear pseudo-differential equations

Abstract

AbstractWe 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) where cη2≤G(η)≤Cη2 for large |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

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Last time updated on 6/4/2019

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