Improved growth estimate of infinite time blowup solution for a semilinear hyperbolic equation with logarithmic nonlinearity

In this short paper, we give an improved estimate of the infinite time blowup solution for the semilinear wave equation with logarithmic nonlinearity. Comparing the previous work, this improved growth estimate not only provides the information about the relationship between the power of the nonlinearity and the growth, but also gives a faster growth estimate. The proof of the main conclusions is carried out at the negative initial energy level, the sub-critical initial energy level, the critical initial energy level and the arbitrary positive initial energy level.