Spatial behavior in high order partial differential equations

Abstract

In this paper we study the spatial behavior of solutions to the equations obtained by taking formal Taylor approximations to the heat conduction dual-phase-lag and three-phase-lag theories, reflecting Saint-Venant's principle. In a recent paper, two families of cases for high order partial differential equations were studied. Here we investigate a third family of cases which corresponds to the fact that a certain condition on the time derivative must be satis ed. We also study the spatial behavior of a thermoelastic problem. We obtain a Phragmén-Lindelöf alternative for the solutions in both cases. The main tool to handle these problems is the use of an exponentially weighted Poincaré inequality.