Existence and asymptotic stability of solutions for a hyperbolic equation with logarithmic source

Abstract

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.