Growth and blow-up of viscoelastic wave equation solutions with logarithmic source, acoustic and fractional conditions, and nonlinear boundary delay

This study focuses on a nonlinear viscoelastic wave equation involving logarithmic nonlinearity. It considers a nonlinear distributed delay influencing the boundary feedback, which is coupled with acoustic and fractional boundary conditions. Following the proof of global existence, we demonstrate the exponential growth and blow-up of solutions with positive initial energy under appropriate assumptions and for a general case of the kernel. This finding broadens and enhances earlier results.