ABSTRACT
This chapter shows the existence of a global attractor for the semiflows generated by two very simple dissipative evolution equations. These are, respectively, a semilinear version of the heat equation, and of the dissipative wave equation. As such, they are a model of, respectively, a parabolic and of a hyperbolic equation. The chapter summarizes the main steps for the construction of the global attractor for the semiflows generated by evolution equations. It introduces the functional space framework and recalls some well known facts on the Laplace operator associated to homogeneous Dirichlet boundary conditions. The chapter briefly considers some aspects of global attractors while proving the so-called upper semicontinuity of the global attractors.
