On the global behaviour of solutions of some fourth order nonlinear equations

Zbere are considered two classes of fourth order nonlinear evolution equations, for first class, included the well known Hahn–Hillard equation, it is proved that there exists a global minimal $B$-attractor, and it is compact and connected, for the second class, included Sivashinsky equation, it is proved a blow-up theorem. In addition, for the Kuramoto–Sivashinsky equation, in one-dimensional case, for even solutions it is prouved the existence of a global minimal $B$-attractor in the fase-space $W_2^1$. Xhis attraetor is compact and connected. In the multi-dimensional case $(n=2,3)$ under some assumption, it is proved the existence of compact attractors for some bounded sets.