Phragmén-Lindelöf Alternative Results for a Class of Thermoelastic Plate

Abstract

The spatial properties of solutions for a class of thermoelastic plate with biharmonic operator were studied. The energy method was used. We constructed an energy expression. A differential inequality which the energy expression was controlled by a second-order differential inequality is deduced. The $Phragm\acute{e}n$-$Lindel\ddot{o}f$ alternative results of the solutions were obtained by solving the inequality. These results show that the Saint-Venant principle is also valid for the hyperbolic–hyperbolic coupling equations. Our results can been seen as a version of symmetry in inequality for studying the $Phragm\acute{e}n$-$Lindel\ddot{o}f$ alternative results.