Lifespan of solutions to a damped fourth-order wave equation with logarithmic nonlinearity

This paper is devoted to the lifespan of solutions to a damped fourth-order wave equation with logarithmic nonlinearity $$u_{tt}+Delta^2u-Delta u-omegaDelta u_t+alpha(t)u_t=|u|^{p-2}uln|u|.$$ Finite time blow-up criteria for solutions at both lower and high initial energy levels are established, and an upper bound for the blow-up time is given for each case. Moreover, by constructing a new auxiliary functional and making full use of the strong damping term, a lower bound for the blow-up time is also derived.