Representations of Slow Integral Manifolds

Abstract

In constructing the asymptotic expansions of slow integral manifolds it is assumed that the degenerate equation ($\varepsilon = 0$) allows one to find the slow surface explicitly. In many problems this is not possible due to the fact that the degenerate equation is either a high degree polynomial or transcendental. In this situation many authors suggest the use of numerical methods. However, in many problems the slow surface can be described in parametric form, and then the slow integral manifold can be found in parametric form as asymptotic expansions. If this is not possible, it is necessary to use an implicit slow surface and obtain asymptotic representations for the slow integral manifold in an implicit form. Model examples, as well as examples borrowed from combustion theory, are treated.