<p>This paper studies a class of nonlinear degenerate parabolic equations involving nonstandard logarithmic source terms. The problem combines degenerate diffusion with reaction terms that lack homogeneity and classical scaling properties, which creates significant analytical difficulties. To overcome these challenges, a suitable logarithmic energy functional is introduced and the potential well method is extended to this generalized framework. Based on this approach, the qualitative behavior of solutions is completely characterized in terms of the initial energy. In particular, global existence of solutions is established for initial data belonging to the stable set, while finite-time blow-up is proved for data in the unstable set. Sharp threshold results are also obtained at critical energy levels. In addition, numerical simulations are performed to support the theoretical findings and to illustrate the influence of logarithmic effects on the solution dynamics. The results provide a unified analytical and numerical framework for degenerate parabolic problems with logarithmic nonlinearities.</p>