ABSTRACT
This chapter introduces the definitions of the SEMIFLOW associated to a dissipative autonomous dynamical system in a Banach space, and of the attractor of this semiflow. It discusses some of the most relevant properties of semiflows and their attractors. The ideas and results presented in the chapter are a natural generalization to the infinite dimensional case of many well known notions of the qualitative theory of ordinary differential equations. The chapter shows that if the semiflow satisfies some compactness assumptions, the existence of an absorbing set is also sufficient for the existence of an attractor. Finally, it presents two results that are commonly used in order to obtain a priori estimates. These results are known, respectively, as the Gronwall’s inequality and the exponential inequality.
