Global Conference on Mathematics and Applications (GCMA)

This paper is concerned with a nonlinear wave equation with logarithmic damping

and logarithmic source terms. Using the Faedo–Galerkin method, compactness tech-
niques, and monotonicity arguments, we establish the local existence and uniqueness

of the solution. We further derive energy estimates to analyze the interplay between
dissipation and nonlinear source effects, proving the finite-time blow-up of the solution
with negative initial energy. The results demonstrate the critical role of logarithmic
damping in solution behavior and improve some existing results in this literature.