Growth and blow-up of solutions for a viscoelastic wave equation with logarithmic source, fractional conditions, and non-linear boundary feedback

This work is concerned with a nonlinear viscoelastic wave equation with logarithmic nonlinearity. By supposing the nonlinear time-varying delay acting on the boundary feedback coupling by the acoustic and fractional boundary conditions. Firstly, we prove the exponential growth of solutions with negative initial-energy under suitable hypotheses and, in general, of the kernel. Then, the blow-up of solutions is showed under the same assumptions. This result extends and complements some previous results.