Infinite Dimensional Problems

Abstract

In this chapter we extend centre manifold theory to a class of infinite dimensional problems. For simplicity we only consider equations of the form

$$ \dot w = Cw + N(w),\,\,\,w(0)\,\, \in \,\,Z $$

where Z is a Banach space, C is the generator of a strongly continuous semigroup on Z and N: Z → Z is smooth. In the next section we give a brief account of semigroup theory. For additional material on semigroup theory see [6,43,50,55, 56]. For generalizations to other evolution systems see [34,51].