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.
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