(untitled) (Journal of Partial Differential Equations, 2025)
This paper considers initial boundary value to a pseudo-parabolic equation with singular potential u_t|x|^s-Δ u_t-Δ u =|u|^p-2u with 2<p<2NN−2, which was studied in [1] by Lian et al. They dealt with the global existence, asymptotic behavior with low initial level J(u_0)≤d and got the blow-up conditions of solutions with low and high initial level. In this paper, we give a new blow-up result which independent of the initial Nehari functional I(u_0), and estimate the lower bound for blow-up time under some conditions. Finally, the precise exponential decay estimate is obtained for global solution with some conditions.