Boundary value problems for strongly degenerate parabolic equations
Mikhail Lavrentiev, Philip Broadbridge, V.Ya. Belov · Communications in Partial Differential Equations · 1997
Solutions of strongly degenerate parabolic partial differential equations are known to develop infinite spatial derivatives in finite time from smooth initial conditions over the real line. However, when Dirichlet or Neumann boundary conditions are prescribed on a finite interval, a smooth classical solution may exist for all Eq., with derivatives vanishing as t tends to infinity. With some simple extra conditions relating two nonlinear coefficients in the degenerate equation, classical solvability is proved in general.