Stabilization of the norm of the solution of a mixed problem in an unbounded domain for parabolic equations of orders 4 and 6

The behaviour as $t\to\infty$ of the solution of a mixed problem for parabolic equations in an unbounded domain with two exits to infinity is studied. A certain class of domains is distinguished, in which an estimate characterizing the stabilization of solutions and determined by the geometry of the domain is established. This estimate is proved to be sharp in a certain sense for a broad class of domains with two exits to infinity.