ABSTRACT
In this paper, we study a three-dimensional (3D) viscoelastic wave equation with nonlinear weak damping, supercritical sources and prescribed past history ,
:
where the relaxation function k is monotone decreasing with ,
and
. When the source is stronger than dissipations, i.e.
, we obtain some finite time blow-up results with positive initial energy. In particular, we obtain the existence of certain solutions which blow up in finite time for initial data at arbitrary energy level.
Notes
No potential conflict of interest was reported by the authors.