  We consider a diffusive transport equation with discontinuous flux and prove
the velocity averaging result under non-degeneracy conditions. In order to
achieve the result, we introduce a new variant of micro-local defect
functionals which are able to ``recognise'' changes of the type of the
equation. As a corollary, we show the existence of a weak solution for the
Cauchy problem for nonlinear degenerate parabolic equation with discontinuous
flux. We also show existence of strong traces at $t=0$ for so-called
quasi-solutions to degenerate parabolic equations under non-degeneracy
conditions on the diffusion term.
