@article{Shi2024, 
author = {Jincheng Shi and Shuman Li and Cuntao Xiao and Yan Liu},
title = {Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {11},
pages = {6235-6257},
keywords = {Phragmén-Lindelöf alternative, quasi-static heat conduction, Saint-Venant's principle, spatial behavior, biharmonic equation},
url = {https://www.sciopen.com/article/10.3934/era.2024290},
doi = {10.3934/era.2024290},
abstract = {This article focused on investigating the spatial behavior of the quasi-static biharmonic conduction equation within the framework of type Ⅲ of the second gradient in a two-dimensional cylindrical domain. The results of growth or decay estimates were established by using a second-order differential inequality. When the distance tends to infinity, the energy either grows exponentially or decays exponentially. The results showed that the Saint-Venant principle was also valid for the quasi-static biharmonic conduction equation.}
}