New Examples of Irreducible Local Diffusion of Hyperbolic PDE's

Abstract

Local diffusion of strictly hyperbolic higher-order PDE's with constant coefficients at all simple singularities of corresponding wavefronts can be explained and recognized by only two local geometrical features of these wavefronts. We radically disprove the obvious conjecture extending this fact to arbitrary singularities: namely, we present examples of diffusion at all non-simple singularity classes of generic wavefronts in odd-dimensional spaces, which are not reducible to diffusion at simple singular points.