Blow-up results for a class of p-Laplacian heat equations with logarithmic nonlinearity
DOI:
https://doi.org/10.24193/subbmath.2026.3.5Keywords:
Pseudo-parabolic equation, logarithmic nonlinearity, variable nonlinearity, blow-up time, bounds of the blow-up timeAbstract
In 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 H1 0 (Ω)-norm as t → +∞. We also give a two-dimensional numerical example to confirm the validity of our theoretical results.
Mathematics Subject Classification (2010): 35B40, 35B44, 35K55.
Received 16 March 2026; Accepted 28 April 2026.
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