@Article{JPDE-33-222,
author = {Long , QunFei},
title = {Bounds for the Blow-Up Time on the Pseudo-Parabolic Equation with Nonlocal Term},
journal = {Journal of Partial Differential Equations},
year = {2020},
volume = {33},
number = {3},
pages = {222--234},
abstract = {<p style="text-align: justify;">We investigate the initial boundary value problem of the pseudo-parabolic equation $u_{t} - \triangle u_{t} - \triangle u = \phi_{u}u + |u|^{p - 1}u,$ where $\phi_{u}$ is the Newtonian potential, which was studied by Zhu et al. (Appl. Math. Comput., 329 (2018) 38-51), and the global existence and the finite time blow-up of the solutions were studied by the potential well method under the subcritical and critical initial energy levels. We in this note determine the upper and lower bounds for the blow-up time. While estimating the upper bound of blow-up time, we also find a sufficient condition of the solution blowing-up in finite time at arbitrary initial energy level. Moreover, we also refine the upper bounds for the blow-up time under the negative initial energy.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v33.n3.3},
url = {http://global-sci.org/intro/article_detail/jpde/17071.html}
}