Inertial Manifolds and Slow Manifolds. The Non-self-adjoint Case

This chapter and the following chapter are based on a presentation of Inertial Manifolds (I.M.) which is different from that contained in Chapter VIII. As we said in the Preface to the Second Edition, Chapters IX and X can be read independently of Chapter VIII. The present chapter contains a presentation of inertial manifolds which is self-contained. The main result of this chapter is an existence result for inertial manifolds (see Theorem 2.1 and also Theorem 3.1) which generalizes Theorem 3.1 of Chapter VIII. Although the results are very similar in cases where both theorems apply, the approach in this chapter offers several advantages.