alternative results for the solutions to generalized heat conduction
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.