Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity

Abstract This paper deals with the initial boundary value problem for strongly damped semilinear wave equations with logarithmic nonlinearity u t t − Δ u − Δ u t = φ p ( u ) log | u | in a bounded domain Ω ⊂ R n . We discuss the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under some appropriate conditions. Moreover, we derive the finite time blow up results of weak solutions, and give the lower and upper bounds for blow-up time by the combination of the concavity method, perturbation energy method and differential–integral inequality technique.