Nonlinear logarithmic wave equations: Blow-up phenomena and the influence of fractional damping, infinite memory, and strong dissipation

This article explores blow-up phenomena in nonlinear logarithmic wave equations with fractional damping, infinite memory, and strong dissipation. The paper proves the existence of a local weak solution using semigroup theory. Furthermore, this research demonstrates that under certain conditions in finite time, the local solution may blow-up by using an appropriate Lyapunov functional. The findings highlight the effectiveness of strong damping, particularly when combined with fractional damping.