In this paper, we prove a blow up result for solutions of the Petrovsky equation with fractional damping term with negative initial energy.

In this work, we investigate the Kirchhoff-type equation with a fractional damping term in a bounded domain. The fractional damping term plays a quenching role, which is weaker than strong damping and stronger than weak damping term. We prove a nonexistence of global solutions with negative inital energy. This result extends and improves some results in the literature.

In this paper, we consider a class of nonlinear higher-order wave equation with logarithmic source and waek damping termWe establish a exponential decay of solutions.