Blow-up of solutions for a nonlinear viscoelastic wave equation with initial data at arbitrary energy level

AbstractIn 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.