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

Abstract

We improve results regarding the stability and attractivity of solutions $u$ of a large class of initial-boundary-value problems characterized by a semi-linear third order equation which may contain time-dependent coefficients. In the proof we use Liapunov functionals $W$ depending on two parameters, which we adapt to the 'error' $\sigma$.