TY - JOUR
T1 - Global and Non-Global Solutions for Pseudo-Parabolic  Equation with Singular Potential
AU - Yang , Chunxiao
AU - Pan , Xinyu
AU - Chen , Yuqing
JO - Journal of Partial Differential Equations
VL - 3
SP - 324
EP - 334
PY - 2025
DA - 2025/09
SN - 38
DO - http://doi.org/10.4208/jpde.v38.n3.5
UR - https://global-sci.org/intro/article_detail/jpde/24404.html
KW - Pseudo-parabolic equation, singular potential, blow-up, bounds for blow up time, exponential decay.
AB - <p style="text-align: justify;">This paper considers initial boundary value to a pseudo-parabolic equation
 with singular potential $\frac{u_t}{|x|^s}-\Delta u_t-\Delta u =|u|^{p-2}u$ with $2&lt;p&lt;\frac{2N}{N−2},$ 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.</p>