Nonexistence of Global Solutions for the Kirchhoff-Type Equation with Fractional Damped

Abstract

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.