The Global Attractors for the Periodic Initial Value Problem of Generalized Kuramoto-Sivashinsky Type Equations in Multi-dimensions

Abstract

The existence of global attractors for the periodic initial value problem of generalized Kuramoto-Sivashinsky type equations in multi-dimensions is proved. We also get the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractors by means of a uniform priori estimates for time.