@article{Yang2022, 
author = {Hui Yang and Futao Ma and Wenjie Gao and Yuzhu Han},
title = {Blow-up properties of solutions to a class of  p-Kirchhoff evolution equations},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {7},
pages = {2663-2680},
keywords = {blow-up, critical exponent, p-Kirchhoff equation, general nonlinearity},
url = {https://www.sciopen.com/article/10.3934/era.2022136},
doi = {10.3934/era.2022136},
abstract = {This paper is devoted to an initial-boundary value problem for a class of  p-Kirchhoff type parabolic equations. Firstly, we consider this problem with a general nonlocal coefficient  M(‖∇u‖pp) and a general nonlinearity  k(t)f(u). A new finite time blow-up criterion is established, also, the upper and lower bounds for the blow-up time are derived. Secondly, we deal with the case that  M(‖∇u‖pp)=a+b‖∇u‖pp,  k(t)≡1 and  f(u)=|u|q−1u, which was considered by Li and Han [Math. Model. Anal. 2019; 24: 195-217] only for  q>2p−1. The threshold results for the existence of global and finite time blow-up solutions to this problem are obtained for the case  1<q≤2p−1, which, together with the results given by Li and Han, shows that  q=2p−1 is critical for the existence of finite time blow-up solutions to this problem. These results partially generalize and extend some recent ones in previous literature.}
}