Explosive for a Damped p-Laplacian-Type Stochastic Wave Equation with Logarithmic Nonlinearity

In this paper, we consider a damped p-Laplacian-type wave equation with logarithmic nonlinearity driven by multiplicative noises. We first establish the local existence and uniqueness of a mild solution to the equation using the truncation technique and semigroup method and show that the local solution is global under certain conditions. Secondly, we show the blow-up properties of solutions using an appropriate energy inequality. Moreover, we also derive estimates of the upper bound of the blow-up time.