@article{Zhao2024, 
author = {Yaxin Zhao and Xiulan Wu},
title = {Asymptotic behavior and blow-up of solutions for a nonlocal parabolic equation with a special diffusion process},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {8},
pages = {22883-22909},
keywords = {logarithmic nonlocal source, special diffusion process, global existence, asymptotic behavior, blow-up},
url = {https://www.sciopen.com/article/10.3934/math.20241113},
doi = {10.3934/math.20241113},
abstract = {This paper considers a class of higher-order nonlocal parabolic equations with special coefficient. We apply the Faedo-Galerkin approximation method and cut-off technique to obtain the local solvability. Furthermore, based on the framework of the modified potential well, we get the global existence, asymptotic behavior, and blow-up of the weak solutions by the Hardy-Sobolev inequality when the initial energy is subcritical  J(u0)<d. In the critical case of  J(u0)=d, the above results have also been obtained. Finally, we utilize some new processing methods to gain the blow-up criterion in finite time with supercritical initial energy  J(u0)>0.}
}