Decay estimate and blow-up for fractional Kirchhoff wave equations involving a logarithmic source

This paper was dedicated to researching a class of fractional Kirchhoff wave models involving a logarithmic source and strong damping term. We have proven the local existence and uniqueness of weak solutions through combining contraction mapping theory with Faedo-Galerkin's method. Based on the framework of a potential well and under suitable conditions, an exponential decay estimate of global weak solutions was established. Finally, the result of the finite time blow-up was obtained.