N. Boumaza, B. Gheraibia, G. Liu, M. Shahrouzi, Kh. Zennir
The main objective of this work is to investigate an initial–boundary value problem for a wave equation incorporating Balakrishnan–Taylor damping, weak damping, and a logarithmic source term. By employing the potential well method combined with an appropriate logarithmic Sobolev inequality, we establish the global existence and energy decay of solutions in the stable set of initial data. In addition, we show that when the initial data lie in the unstable set, the corresponding solutions blow up in infinite time in the cases $ E(0)<d $ and $ E(0)<0 $. These results provide a comprehensive description of the long-term behavior of solutions, highlighting the balance between dissipative effects and the logarithmic nonlinearity.