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 3‐phase‐lag theories, reflecting Saint‐Venant's principle. In a recent paper, 2 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 satisfied. 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.
Mathematical Methods in the Applied Sciences – Wiley
Published: Jan 1, 2018
Keywords: ; ;
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