Qualitative properties for a class of non-autonomous 3-rd order semi-linear PDE arising in dissipative problems

We prove new results regarding the existence, uniqueness, boundedness, stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a semi-linear third order equation which may con- tain time-dependent coefficients. The class includes equations arising in Su- perconductor Theory and in the Theory of Viscoelastic Materials. In the proof of boundedness, stability and attractivity we use a family of Liapunov functionals W depending on two parameters, which we adapt to the ‘error’, i.e. to the size σ of the chosen neighbourhood of the solution.