Local Decomposition and Accessibility of PDE Systems

The local decomposition of (nonlinear) ODE systems, which is obtained in the presence of a codistribution invariant under the system vector field and an associated local partition of the underlying manifold, is well-studied in the literature, and its relevance w.r.t. the local accessibility problem is indisputable. In this contribution we focus on the local decomposition of (nonlinear) PDE systems. In particular, it is shown that in the presence of a codistribution invariant under the so-called generalized system vector field a triangular decomposition, including the decomposition of the boundary conditions under certain conditions, can be obtained. In addition, we highlight the geometric picture behind our approach and that these results can be applied to the accessibility problem, where conditions for the local decomposition of a (non-accessible) system into subsystems are provided. A nonlinear example illustrates the results.