Existence, uniqueness and stability for a class of third-order dissipative problems depending on time

Abstract 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.