Abstract: We considered  a class of Kirchhoff type viscoelastic wave equation with logarithmic nonlinear term of variable exponents. Firstly, the energy identity for the problem was given. Secondly, by constructing auxiliary functions and using Holder inequality and Gagliardo-Nirenberg inequality, we obtained the result of blow up of equation solutions in finite time in the case where  the logarithmic nonlinear term  contained variable exponents.

Key words: Kirchhoff type equation, viscoelastic wave equation, logarithmic nonlinearity, variable exponent, blow up