Phragmén–Lindelöf type alternative results for the solutions to generalized heat conduction equations

Abstract

This paper investigates the spatial behavior of the solutions of the generalized heat conduction equations on a semi-infinite cylinder by means of a first-order differential inequality. We consider three kinds of semi-infinite cylinders with boundary conditions of Dirichlet type. For each cylinder, we prove the Phragmén–Lindelöf alternative for the solutions. In the case of decay, we also present a method for obtaining explicit bounds for the total energy.