  Aim of the paper is the qualitative analysis of a quasi-linear parabolic
third order equation, which describes the evolution in a large class of
dissipative models. As examples of some typical boundary problems, both
Dirichlet's and Neumann's type boundary conditions are examined. In the linear
case, the related Green functions are explicitly determined, together with
rigorous estimates of their behavior when the parameter of dissipation is
vanishing. These results are basic to study the integral equations to which the
non linear problems can be reduced. Moreover, boundary layer estimates can be
determined too.
