Abstract:

The transient heat conduction equation defined in a three-dimensional semi-infinite cylinder is Considered, in which the nonlinear conditions are imposed on the finite end and the lateral surface of the cylinder. A partial differential inequality for the "energy expression" is established after some constraints are imposed on the boundary conditions, and Phragmén-Lindelöf type results of the heat conduction equation is obtained from the inequality. In the case of decay, it is proved that "total energy" can be controlled by known data.

Key words: Heat conduction equation, Spatial decay estimates, Phragmén-Lindelöf, Energy estimates