  We prove new results regarding the existence, uniqueness, (eventual)
boundedness, (total) stability and attractivity of the solutions of a class of
initial-boundary-value problems characterized by a quasi-linear third order
equation which may contain time-dependent coefficients. The class includes
equations arising in Superconductor Theory and in the Theory of Viscoelastic
Materials. In the proof we use a Liapunov functional V depending on two
parameters, which we adapt to the characteristics of the problem.
