BOUNDARY-VALUE-PROBLEMS FOR STRONGLY DEGENERATE PARABOLIC EQUATIONS

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.