On degenerate parabolic equations with dynamic boundary conditions

We wish to present some recent developments concerning the
solvability of some classes of quasilinear parabolic equations with
dynamic boundary conditions. We will describe issues from
well-posedness to the long time asymptotic behavior as time goes to
infinity (attractors, dimension estimates, etc). We will explain how
to derive new conditions which reflect an exact balance between the
internal and the boundary mechanisms involved, even when both the
nonlinear sources contribute in opposite directions. Blow up of
solutions will also be touched on.