I am reading a paper on degenerate parabolic PDE and I am confused about the following statement.
" Diffusion coefficient is $mu^{m-1}$, and it vanishes when $u=0$. Hence at all those points where $u=0$ equation looses parabolicity, or degenerate, and accordingly classical theory of uniformly parabolic equation is not applicable
I don't understand this. What does classical theory of uniformly parabolic equation mean? How does it work? When does it fail?