A characteristic initial boundary value problem for a symmetric positive system

We study the simplest maximal positive boundary value problem for symmetric positive systems in a bounded open set for which the boundary matrix is not of constant rank. To be precise, the boundary matrix changes the definiteness simply crossing an embedded manifold in the boundary which is the intersection of the boundary with a non-characteristic hypersurface. Assuming that the flow passing the hypersurface compensates for the degeneracy of the boundary matrix on the embedded manifold, we discuss the existence of regular solutions to the boundary value problem.