Razik, BelhaouesBiccari, UmbertoAbita, Rahmoune2026-10-062026-10-062026-09-07Belhaoues, R., Biccari, U., & Abita, R. (2026). Blow-up results for a class of p-Laplacian heat equations with logarithmic nonlinearity. Studia Universitatis Babes-Bolyai Mathematica, 71(3), 399-420. https://doi.org/10.24193/SUBBMATH.2026.3.50252-193810.24193/SUBBMATH.2026.3.5https://hdl.handle.net/20.500.14454/6750In this paper, we consider an initial-boundary value problem for the following mixed pseudo-parabolic p(.)-Laplacian type equation with logarithmic nonlinearity on a bounded and regular domain. By adapting the first-order differential inequality method, we establish a blow-up criterion for the solutions and obtain an upper bound for the blow-up time. Besides, we show that blow-up may be prevented under appropriate smallness conditions on the initial datum, in which case we also establish decay estimates in the H10(Ω)-norm as t → +∞. We also give a two-dimensional numerical example to confirm the validity of our theoretical results.eng© Studia UBB MATHEMATICABlow-up timeBounds of the blow-up timeLogarithmic nonlinearityPseudo-parabolic equationVariable nonlinearityjournal article2026-10-062065-961X