Global existence and blow up of solution of wave nonlinear equation with boundary fractional damping and logarithmic source terms

In this study, a global solution is presented for an initial boundary value problem involving a wave equation with logarithmic nonlinear source terms and fractional boundary dissipation. The solution is obtained through the application of the energy method combined with the Faedo-Galarkin procedure. Additionally, a blow-up result for the solution is established, contingent upon the condition of non-positive initial energy.