TY - JOUR
T1 - Blow-Up Phenomena for Some Pseudo-Parabolic Equations with Nonlocal Term
AU - Liu , Gongwei
AU - Tian , Shuying
JO - Analysis in Theory and Applications
VL - 4
SP - 451
EP - 466
PY - 2023
DA - 2023/01
SN - 38
DO - http://doi.org/10.4208/ata.OA-2019-0021
UR - https://global-sci.org/intro/article_detail/ata/21359.html
KW - Nonlocal pseudo-parabolic equations, blow-up, upper bound, lower bound.
AB - <p style="text-align: justify;">We investigate the initial boundary value problem of some semilinear pseudo-parabolic equations with Newtonian nonlocal term. We establish a lower bound for the blow-up time if blow-up does occur. Also both the upper bound for $T$ and blow up rate of the solution are given when $J(u_0)&lt;0$. Moreover, we establish the blow up result for arbitrary initial energy and the upper bound for $T$. As a product, we refine the lifespan when $J(u_0)&lt;0.$</p>