MANIFOLDS OF SLOW SOLUTIONS FOR HIGHLY OSCILLATORY PROBLEMS

We consider stiff oscillatory systems of ordinary differential equatio ns and ask for slowly varying solutions. As is well-known, if the init ial data are chosen by the bounded derivative principle, then the solu tion varies slowly up to some order. In this paper we clarify the rela tion between the bounded derivative principle and the existence of a l ocal or global slow manifold. The manifolds are obtained by solving a first-order system of partial differential equations. Also, we estimat e the interaction between the fast and the slow scale for solutions wh ich start off the slow manifold.