In this paper, we consider a hyperbolic equation with a logarithmic source term. This work is devoted to prove the global existence and the uniform energy decay rates of a weak solution applying the logarithmic Sobolev inequality and modified multiplier method. This result gives us to classify the energy decay rate dependent on the growth near zero on the damping term.

中文翻译：

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一类对数源双曲方程解的存在性和渐近稳定性

在本文中，我们考虑具有对数源项的双曲方程。这项工作致力于应用对数 Sobolev 不等式和改进的乘数法证明弱解的全局存在性和均匀能量衰减率。这个结果使我们能够根据阻尼项上接近零的增长对能量衰减率进行分类。