On Fractal Dimension of Global and Exponential Attractors for Dissipative Higher Order Parabolic Problems in $$\mathbb {R}^N$$ with General Potential

Abstract

We consider a Cauchy problem for a dissipative fourth order parabolic equation in \(\mathbb {R}^N\) with a general potential. Using the method by Chueshov and Lasiecka we estimate from above fractal dimension of a global attractor. We also show that it is contained in a finite dimensional exponential attractor.