M. Lavrentiev et al., BOUNDARY-VALUE-PROBLEMS FOR STRONGLY DEGENERATE PARABOLIC EQUATIONS, Communications in partial differential equations, 22(1-2), 1997, pp. 17-38
Solutions of strongly degenerate parabolic partial differential equati
ons are known to develop infinite spatial derivatives in finite time f
rom smooth initial conditions over the real line. However, when Dirich
let or Neumann boundary conditions are prescribed on a finite interval
, a smooth classical solution may exist for all t greater than or equa
l to 0, with derivatives vanishing as t tends to infinity. With some s
imple extra conditions relating two nonlinear coefficients in the dege
nerate equation, classical solvability is proved in general.