  The purpose of this paper is twofold. First we study a class of Banach
manifolds which are not differentiable in traditional sense but they are
quasi-differentiable in the sense that a such Banach manifold has an embedded
submanifold such that all points in that submanifold are differentiable and
tangent spaces at those points can be defined. It follows that differential
calculus can be performed in that submanifold and, consequently, differential
equations in a such Banach manifold can be considered. Next we study the
structure of phase diagram near center manifold of a parabolic differential
equation in Banach manifold which is invariant or quasi-invariant under a
finite number of mutually quasi-commutative Lie group actions. We prove that
under certain conditions, near the center manifold $\mathcal{M}_c$ the
underline manifold is a homogeneous fibre bundle over $\mathcal{M}_c$, with
fibres being stable manifolds of the differential equation. As an application,
asymptotic behavior of the solution of a two-free-surface Hele-Shaw problem is
also studied.
