@article{Almuthaybiri2024, 
author = {Saleh Almuthaybiri and Tarek Saanouni},
title = {Energy solutions to the bi-harmonic parabolic equations},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {35264-35273},
keywords = {inhomogeneous fourth-order parabolic problem, nonlinear equations, global/non-global solutions},
url = {https://www.sciopen.com/article/10.3934/math.20241675},
doi = {10.3934/math.20241675},
abstract = {This study explores the threshold of global existence and exponential decay versus finite-time blow-up for solutions to an inhomogeneous nonlinear bi-harmonic heat problem. The novelty is to consider the inhomogeneous source term. The method uses some standard stable sets under the flow of the fourth-order parabolic problem, due to Payne-Sattynger.}
}