Considered herein is the well-posedness, asymptotic stability and blow-up of the initial-boundary value problem for nonlocal singular viscoelastic wave equation with logarithmic nonlinearity \(u_{tt}-\frac{1}{x}(x u_{x})_x-\frac{1}{x}(x u_{xt})_x+\int \limits _{0}^{t}m(t-\lambda )\frac{1}{x}(x u_{x}(x, \lambda ))_x \hbox {d}\lambda =|u|^{r-2}u\ln |u|\) subject to a nonlocal boundary condition. Through the effective combining of Galerkin approximation method, modified potential well theory, perturbed energy method, convexity theory and differential-integral inequality techniques, we firstly demonstrate the global existence and uniqueness of weak solutions in certain weighted Sobolev spaces; Secondly, we establish the explicit polynomial and exponential energy decay estimates under some suitable conditions; Finally, we investigate the finite time blow-up criterion and then derive its upper and lower bounds of blow-up time. The above conclusions extend and improve some results in the literatures.
