Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ

Abstract

<p>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.</p>