Global attractor for sectorial evolutionary equation (Q1910861)

Let \(A\) be a sectorial operator with compact resolvent in an appropriate Banach space and consider the evolution equation \(\dot u + Au = F(u)\), \(t > 0\), \(u(0) = u_0\). The authors show that this problem generates a dissipative semigroup whenever an appropriate introductory estimate for solutions is known. Such an estimate is then shown to be sufficient for existence of a global attractor. Examples illustrate the authors ideas.