ATTRACTOR OF THE GENERALIZED SEMIGROUP GENERATED BY AN ELLIPTIC EQUATION IN A CYLINDRICAL DOMAIN
Anatoli V. Babin · Izvestiya Mathematics · 1995
In a domain the elliptic system is considered with a Neumann boundary condition. denotes the set of solutions of this system defined for , equal to for , and bounded in uniformly for . In the space of initial data there arises the semigroup , , wherein to the point there is assigned the set , i.e., is a multivalued mapping. In the paper it is proved that has a global attractor . A theorem is proved that where is the set of solutions of the elliptic system, defined and bounded for .