中文摘要：

该文考虑一类具对数源项波动方程的初边值问题.利用Galerkin方法结合对数Sobolev不等式和对数Gronwall不等式,对所有初始值得到了整体解的存在性.通过引入位势井,给出了解在时间无穷远处爆破（即指数增长）的充分条件.当具有对数源项的波动方程还带有线性阻尼时,通过构造适当的Lyapunov函数,得到了能量的衰减估计.

英文摘要：

In this paper we consider the initial boundary value problem for a class wave equation with logarithmic source term. By using Galerkin method combining with the logarithmic Sobolev inequality and logarithmic Gronwall inequality, we obtain the existence of global solution for all initial data. By introducing potential well theory, we give the sufficient condition of the blow-up property in infinity time （i.e. exponential growth） of the solution. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for the wave equation with logarithmic source term and linear damping term.