On the large time behavior of solutions of fourth order parabolic equations and ε-entropy of their attractors

We study the large time behavior of solutions of a class of fourth order parabolic equations defined on unbounded domains. Specific examples of the equations we study are the Swift-Hohenberg equation and the Extended Fisher-Kolmogorov equation. We establish the existence of a global attractor in a local topology. Since the dynamics is infinite dimensional, we use the Kolmogorov epsilon-entropy as a measure, deriving a sharp upper and lower bound.