  We develop the attractors theory for the semigroups with multidimensional
time belonging to some closed cone in an Euclidean space and apply the obtained
general results to partial differential equations (PDEs) in unbounded domains.
The main attention is payed to elliptic boundary problems in general unbounded
domains. In contrast to the previous works in this direction our theory does
not require the underlying domain to be cylindrical or cone-like or to be shift
semi-invariant with respect to some direction. In particular, the theory is
applicable to the exterior domains.
